Initiate a Research Group on Differential Equations, Dynamical Systems, Geometry and Topology
with the intention of growing to become a Research Center, as achieved in 1990

In 1984 Luis Magalhães created a Research Group as a new Research Line of the CMAF – Center for Mathematics and Fundamental Applications, at the IFM – Institute of Mathematical Physics, the Interdisciplinary Complex II of the INIC - Instituto Nacional de Investigação Científica, with the intention of being the embryo of a future Research Center on the mentioned fields, aiming to initiate a weekly Research Seminar on the considered fields with internal presentations and a frequent participation of foreign visitors, to organize international conferences and to host a Post-Docs Program recruited worldwide. Initially, in 1984, it had only 3 IST members: Luis Magalhães (the only PhD), Manuel Ricou, João Palhoto Matos and 1/3 member shared with other Research Line of CMAF (José Francisco Rodrigues of the Faculty of Sciences of U. of Lisbon).

In 1985, Carlos Rocha, returning from Brown University were he obtained his PhD also with Jack Hale, joined this Research Group, and Manuel Ricou, who had returned to Portugal in 1983 after defending orally his PhD thesis but without submitting it in writting at the time, obtained his PhD from U. of Minnesota.

In 1986, Luis Magalhães and Carlos Rocha presented to the IST Scientific Council Coordination Committee a project proposal for the creation and initial equipment of a Computing Laboratory on Dynamical Systems, which was approved and funded. The idea was to develop numerical and symbolic methods for the support of the Geometric Theory of Nonlinear Dynamical Systems, a pioneering idea at the time in few reserch groups worldwide. One of the first students to work in this laboratory was Miguel Abreu, who was completing the recently created undergraduate degree in Applied Mathematics and Computing (a 5 years program) and in 1996 took his PhD at Stanford U. and later on became Full Professor at the IST Department of Mathematics.

In 1988, this Research Group decided to move the Research Line to CAPS – Center for Signal Analysis and Processing, of the Interdisciplinary Complex I of INIC at IST, now already with 9 members of whom 5 PhDs (Luis Magalhães, Manuel Ricou, Carlos Rocha, Pedro Gonçalves Henriques and Luís Canto de Loura, the latter two with recent PhD by U. of Wisconsin-Madison and U. of Houston). At CAPs grew a strong alliance of our Research Group with João Sentieiro and the associated Signal Analysis and Control group of the IST Department of Electrical and Computer Engineering (DEEC) and also a Research Line of CAPS.

The CAPS was a legacy of Abreu Faro, an influential Professor of Telecommunications at the IST Department of Electrical and Computer Engineering, had recently spinned off the INESC- Institute of Engineering Systems and Computers (later on approved as Associate Laboratories by FCT - Science and Technology Foundation), and was the Center of other determinant researchers for the development at IST of Systems and Signal Processing, Control, Robotics, Pattern Recognition, Machine Learning, in particular José Manuel Fonseca de Moura, João Sentieiro, José Manuel Leitão (also a very close colleague from the time at the Physiology Lab of the IGC - Gusbenkian Institute of Science), Luis Borges de Almeida, among others. In 1990 CAPS also spinned off the ISR-System of Systems and Robotics, the IT-Institute of Telecommunications (both later on approved as Associate Laboratories by FCT, and our Center of Mathematical Analysis, Dynamical Systems and Applications to Engineering. Our Research Group, that in the meanwhile had further grown, participated with about half of its members integrating this Center and the other half integrating the ISR. This close relationship of our Research Group with an important part of the IST Department of Electrical and Computer Engineering (DEEC) was of decisive strategic importance in the IST internal politics to achieve a sufficiently wide acceptance and support on initiatives of the IST Mathematics Department.

In 1990, Luis Magalhães led the creation of the Center for Mathematical Analysis, Dynamical Systems and Applications to Engineering with a team formed by part of the Research Group created on these fields in 1985, with basis on a three-year project that was approved for funding by the CIENCIA Program managed by JNICT and oriented to fund science infrastructures. This project allowed to equip the Center members with personal computers, to set up an Ethernet network providing internal and external computer connectivity, and to acquire research journals assuring a nice reserach library in the considered fields.

In 1990, Luis Magalhães also joined João Sentieiro and Isabel Ribeiro, both of CAPS and the IST Department of Electrical and Computer Engineering (DEEC), in jointly leading a proposal for the creation of the ISR – Institute of Systems and Robotics, also sibmitted to the CIENCIA Program, and also for a period of three years. This institute proposal also involved a team of the Faculty of Science and Technology of U. of Coimbra led by Aníbal Traça de Almeida, and a team of the Faculty of Engineering of the U. of Porto led by Jorge Martins de Carvalho. This was a much more ambitious venture, due to its national character and dimension, that required a strenuous strategic and coordination effort of João Sentieiro and Luis Magalhães, but it brilliantly succeeded on being approved for funding, with the participation of part of the Research Group on Differential Equations, Dynamical Systems, Geometry and Topolgy essential to strengthn the IST component.

Thus, the Research Group, now with 16 members of which about 8 PhDs, was in 1990 formally split in about half of its members in each one of these two new Research Units, with those in the ISR-Lisbon team about 1/3 of all team members, with Luis Magalhães in both, as Director of the Center and Adjunt Director of the ISR-Lisbon.

In 1993/94, due to the termination of the INIC - National Institute of Scientific Research, supporting research centers at universities, the Research Group left CAPS and both the Center and ISR submitted proposals to the Pluriannual Funding Program of R&D Units, opened by the National Boead for Scientific and Technological Research (JNICT) to cover the basic funding of research centers following the termination of the INIC, and with national evaluation panels. They were both approved for funding and were classified at the top rank then adopted by JNICT. A major strategic decision at that time was to have the IST Department faculty separated in different R&D Units instead of trying to organize them in only one R&D Unit. The rationale for this was: This strategy proved throughout decades to be most effective.

In 1995, it was decided to unify the whole Research Group, now with 54 member of whom 24 with PhD, into the Center, and, by proposal of Luis Magalhães to change its name to Center for Mathematical Analysis, Geometry and Dynamical Systems (CAMGSD), since the return to Portugal of its members who took PhDs in areas of Geometry and Topology already provided the grounds for a Research Center with this scope.

in 1997 the CAMGSD had 72 members, of whom the following 29 PhDs: Besides, 16 CAMGSD members where studying for their PhDs abroad:
In just 13 years, the Research Group increased from just 3 members of whom only 1 PhD (Luis Magalhães) in 1983, to 72 members of whom 29 with PhDs in 1997 (accounting for more than half of the IST Mathematics Department faculty holding a PhD), and with 16 of its members studying for a PhD at top universities abroad, ensuring the conditions for the Research Group to more than double its PhD members and reach more than 80 PhDs by 2002 (i.e. more than 80% of its current size in 2026).
83% of the PhDs had been obtained abroad in 22 world top universities in Mathematics, advised by a diversified group of leading mathematicians,
2/3 of them had done their undergraduate studies in Engineering or Physics before taking a PhD in Mathematics (28% in Physics, 24% in Electrical Engineering, 7% in Civil Engineering, 7% in Chemical Engineering), making for a remarkable an enviable Research Group experience and diversity.
1/3 of the member who held a PhD or were studying abroad for a PhD had obtained the undergraduate degree at the IST Mathematics 5 years long Undergraduate program LMAC, initiated in 1986 with a strong involvement of the Researh Group senior members;
2/3 of them had been encouraged to go abroad for PhD degrees, most insistently by Luis Magalhães, but also by other senior Research Group members who sponsored and supervised them at IST:
Evolution of the Number of the Research Group Created in 1983 to Develop to a Research Center (CAMGSD) in Luis Magalhães Tenure as Coordinator (1983-97)
CMAF - Center of Mathematics and Fundamental Applications (Complex II of INIC, IFM),     CAPS - Center of Signal Analysiis and Processing (Complex I of INIC, IST)
CAMSDAE - Center for Mathematical Analysis, Dynamical Systems and Engineering Applications,     ISR, Lisbon - Isntitute of Systems and Robotics, Lisbon
CAMGSD - Center for Mathematical Analysis, Geometry and Dynamical Systems
EvolutionSAAStaff
In the 1st of May 1997, Luis Magalhães, who led the Research Group since he had created it in 1984 with only 3 members and only him with PhD, to reach 72 members of whom 29 PhDs and with 16 members taking their PhDs broad (13 at USA universities, 2 at U. of Oxford and 1 at U. of Cardiff), was invited by the Minister of Science and Technology, José Mariano Gago, to be the 1st President of the then created FCT - Science and Technology Foundation. This invitation was received with mixed feelings and was not accepted immediatly; he asked 4 days to think about it, but ended up accepting at the last minute, by 24:00 of a Sunday deadline, when Armando Trigo de Abreu, the Minister Chief of Staff and an old acquaintance from the time at the IGC - Gulbekinan Institute of Science, called for a soft pressure as a friend.

The hesitation was because the Research Group created was reaching a high level of considerable size and it was time to reap the benefits of the several years labour on one of the most important points of the 1983 draft Strategic Plan, and for which a flourishing period could be antecipated with the concentrated return of so many talented young PhDs taken at top universities, being clear that leading the Research Group in the near future would be exciting and a great joy. On the other hand the new position was for a very interesting challenge which could be antecipated to have a huge impact in developing national scientific and technological research in all areas, which at the time was insipient. Moreover, it would be an administration function at the center of the Government bureaucracy, very different from academic administration and it was not clear if this could be coped with. Besides it would imply to abandon personal scientific research and this was a radical personal decision. The invitation ended up being accepted due to a total sintony with the Minister intentions for the National Science and Technology (S&T) Policy, aiming to develop Portuguese research to a high international level, and by personal solidarity with the Minister nourished, as colleagues, since when he was an admirable President of the IST Student Union and later on consolidated as IST faculty collegues in the periods 1983-86 and 1989-95, when he was the President of the National Board for Scientific Research (JNICT) in 1986-89, and also in his initial years as Minister of Science and Technology since October 1985 by participating in a very restricted informal advisory group with weekly meetings he created and by coordinating the 1st national international assessment of all the Portuguese R&D Units by appointment of him.

Thus, at the beginning of July 1997, Luis Magalhães, left the CAMGSD leadership to Carlos Rocha, who assured it brilliantly for more than two decades, up to retiring for health reasons in 2020.

In October 2004, FCT invited R&D Research Units of specific scientific areas (not including Mathematics) to present proposals for new Associate Laboratories, although the legislation of 1999 that enacted this type of research organization established that it could be requested at any time by any R&D Research Unit evaluated and funded by FCT. Luis Magalhães, who had resigned from President of the FCT - Science and Technology Foundation after 5 years tenure and had returned to IST and the CAMGSD in July 2002 at the beginning of a new Government with whom he anticipated could not work (and indeed the next 3 years were a disaster for National S&T Policy), suggested to Carlos Rocha that, giving that FCT was willing to synchronize the attribution of the Associate Laboratory statute to several new R&D Units at that time, the CAMGSD should present then a request of the Associate Laboratory statute, since the related extra finantial resources could enable to expand the Post-Doc Program, the PhD Program and its internationalization in the Center areas, the foreign scientists visiting program, and provide resources for hiring full-time Researchers.

This suggestion was approved by the CAMGSD and a request of the Associate Laboratory statute was prepared, coordinated by Luis Magalhães who was its main writer and proposed to formally expand the Center research areas to Mathematical Physics and to invite the IST Mathematics Department professors working in this area who were not members of the CAMGSD to join this Center. Still in October 2004, Luis Magalhães and Rui Loja Fernandes subscribed individual proposals for admission to the CAMGSD of José Mourão, Roger Picken and Carlos Florentino and their students, were they would join João Pimentel Nunes, a long time Center member with whom they collaborated regularly; the proposals were individually voted by the Center members and all of them were accepted. This group developed further in the following years and assumed a visible role in the Center management and in several important new initiatives.

The request was submitted to FCT in October 2004 and addressed to the Minister of Science, Technology and Higher Education, Maria da Graça Carvalho, as established by Law, but an answer was never received either from the Minister or from FCT, against the Law establishing that all such requests must receive a justified answer; and worst, it was not even sent to scientific evaluation! This, in spite of it being very clearly stated in the request initial pages that:
To illustrate how the IST Mathematics Department faculty got involved in different R&D Units, according to the IST Mathematics Department Research Reports of 2007 and 2008 (the last years when this series was published), IST Mathematics Department faculty were members of the following main R&D Units in 2008: and 1 or 2 persons of the IST Mathematics Department faculty were members of each one of the following other R&D Units: Naturally, these associations of IST Mathematics Department faculty with R&D Units in 2008 changed somewhat before and after 2008. It is included here just to illustrate with a concrete observation the result of the above mentioned strategic decision of participation of the Department faculty in diverse R&D Units, assumed when the FCT - Science and Technology Foundation E&D Units Pluriannual Funding Program was initiated in 1994.

In 2012, Luis Magalhães returned to IST and the CAMGSD (now as Collaborator and not Permanent Member of this Center). The CAMGSD counted then with more than 75 PhDs (including Post-Docs), of which 64 were Permanent Members and the others Collaborators, being the largest Mathematics Research Unit in Portugal, and its main areas of activity were: which together accounted for approximately 86% of the Center permanent members. The 7 foreign members of the former IST Algebra and Analysis Section were all members of this Center.
In the international scientific journals of the American Mathematical Society's MathSciNet database, which refers to more than 2,000 journals in Mathematical Sciences and Applications, in 2011 the Center, which had about 12% of the researchers from all Mathematics units in the country, published 15% of the total articles from Portugal, but more relevantly, in the top 10, 20, 60, and 100 journals in MathSciNet, the percentage of articles from the Center in the country's total rised to, respectively, 100%, 60%, 33%, and 33%! In addition, the Center published 42% of the total articles from Portugal in the Center's main areas, corresponding to 82% of its members: Dynamical Systems, Differential Equations, Calculus of Variations, Mathematical Physics, Symplectic/Differential Geometry, Algebraic Topology, and Operator Algebras. In these areas, the percentage of articles from the Center in the national total in the top 60 and 100 journals was, in 2011, respectively, 42% and 35%.

In 2013 FCT announced it would promote a new international assessment of all R&D Units it was funding and that the evaluation of the Associate Laboratories would be done by the evaluation panel of its main area, which for LARSys was Engineering, even if they included individualized R&D Units of other areas. This posed a serious problem to CAMGSD since it should be evaluated as a Mathematics Research Center, forcing it to leave LARSys and present itself to the launched evaluation independently, being again classified Excellent.

In 2016 the then Minister of Science, Technology and Higher Education, Manuel Heitor, invited Luis Magalhães to Coordinate the 2017 international assessment of Portuguese R&D Units, with the aim of recovering from the disastrously designed 2013 assessment in a previous Goverment period which had received widespread criticism of the Portuguese Research Community and led to discredit the assessment. This invitation was accepted under the condition that the coordination would be done by a Committee of 4 persons of different research areas he would propose, Chaired by him, and that radically different Rules to be prepared by this Committee would be formally adopted for the assessment. At the same time, Luis Magalhães left the CAMGSD to be out of the national R&D Units to be assessed and never rejoinned the Center he had created.

In 2024 the CAMGSD had 92 PhD members distributed by the following main research areas:

The areas of research activity of the CAMGSD members included: harmonic analysis, functional analysis, operator algebras, qualitative theory of dynamical systems, geometric mechanics and Hamiltonian systems, nonlinear analysis, ergodic theory, stochastic analysis, partial differential equations, calculus of variations, algebraic geometry, algebraic topology, category theory, differential topology, differential geometry, symplectic geometry, discrete geometry, general relativity, quantum field theory, string theory, statistical mechanics.

In 1998-2024, the CAMGSD hosted more than 130 PostDoc Fellows or PhD Researchers in temporary contracts, contributing to career development of mathematicians through a fully internationalized program, by far the largest such program in Mathematics and one of the largest in all scientific areas in Portugal. The service of this Research Group to the IST Mathematics Department and to the IST as a whole was rendered in manifold capacities and it is concisely illustrated by:
The service of this Research Group to the National Scientific and Technologial policy was also remarkable, mainly through the several national assigments of Luis Magalhães in a total of more than 12 years of intensive full-time service (about 1/3 if his professional career), the service of Carlos Rocha in the National S&T Council and in several FCT evaluation panels, and the service of João Palhoto Matos as full time Advisor for Information Processing of the FCT Board of Directors from June 2007 to September 2011, among others.

The CAMGSD is presently the only Mathematics Research Unit in Portugal funded by the FCT classified Excellent in all the 7 international evaluations that FCT promoted, in 1996, 1999, 2002, 2007, 2013, 2017, 2023 (a few other Research Units of Mathematics were classified Excellent in some of the evaluations but none other in all).

For information on the quality of research results published by this Research Group researchers, are chosen below the articles published in high impact Mathematics journals, in particular of the Web of Science-Clarivate Core Collection, with high nonself citations in this Collection. The number of nonself citations of an article in the Web of Science-Clarivate Core Collection, is a good proxy indicator of the quality of the research reported in the article, since it is driven by how useful the article was to the work of other researchers, what should be the main reason to publish. Like all other bibliometric indicators, it is not perfect, e.g. it is not immune to citation syndicates, it depends on the the number of researchers in the subarea of research and it is an indirect indicator of research relevance and quality, but it is an incomparably better indicator of reasearch quality of articles than other simple widely used bibliometric indicators.
The CAMGSD members published the following highly cited Mathematics articles (>100 nonself citations) in the Web of Science-Clarivate Core Collection of journals (CAMGSD members at the time of publication are in bold):
  1. 388 nonself citations: Faria, Teresa; Magalhães, Luis T., Normal Forms for Retarded Functional Differential Equations with Parameters and Applications to Hopf Bifurcation, Journal of Differential Equations, 122 (1995), 181–200.
  2. 349 nonself citations: Ashtekar, Abhay; Lewandowski, Jerzy; Marolf, Donald; Mourão, José; Thiemann,Thomas, Quantization of diffeomorphism invariant theories of connections with local degrees of freedom, Journal of Mathematical Physics, 36 (1995), 6456–6493.
  3. 290 nonself citations: Faria, Teresa; Magalhães, Luis T., Normal Forms for Retarded Functional Differential Equations and Applications to Bogdanov-Takens Singularity, Journal of Differential Equations, 122 (1995), 201–224.
  4. 254 nonself citations: Crainic, Marius; Loja Fernandes, Rui, Integrability of Lie brackets, Annals of Mathematics, 157 (2003), 575–620.
  5. 245 nonself citations: Gomes, Diogo A.; Saúde, João, Mean Field Games Models-A Brief Survey, Dynamic Games and Applications, 4 (2014), 110–154.
  6. 225 nonself citations: Barreira, Luís; Schmelling, Jorg, Sets of "non-typical" points have full topological entropy and full Hausdorff dimension, Israel Journal of Mathematics, 116 (2000), 29–70.
  7. 188 nonself citations: Noris, Benedetta; Terracini, Susana, Tavares, Hugo; Verzini, Gianmaria, Uniform Hölder Bounds for Nonlinear Schrödinger Systems with Strong Competition, Communications on Pure and Applied Mathematics, 63 (2010), 267–302.
  8. 157 nonself citations: Abreu, Miguel, Kahler geometry of toric varieties and extremal metrics, International Journal of Mathematics, 9 (1998), 641–651.
  9. 156 nonself citations: Loja Fernandes, Rui, Lie algebroids, holonomy and characteristic classes, Advances in Mathematics, 170 (2002), 119–179.
  10. 153 nonself citations: Gomes, Diogo A.; Mohr, Joana; Souza, Rafael Rigão, Discrete time, finite state space mean field games, Journal de Mathématiques Pures et Appliquées, 93 (2010), 308–328.
  11. 142 nonself citations: Barreira, Luís, A non-additive thermodynamic formalism and applications to dimension theory of hyperbolic dynamical systems, Ergodic Theory and Dynamical Systems, 16 (1996), 871–927.
  12. 115 nonself citations: Crainic, Marius; Loja Fernandes, Rui, Integrability of Poisson brackets, Journal of Differential Geometry, 66 (2004), 71–137.
  13. 106 nonself citations: Barreira, Luís; Saussol, Benoit, Variational principles and mixed multifractal spectra, Transactions of the American Mathematical Society, 353 (2001), 3919–3944.
  14. 103 nonself citations: Barreira, Luís; Saussol, Benoit, Hausdorff dimension of measures via Poincare recurrence, Communications in Mathematical Physics, 219 (2001), 443–463.
  15. 102 nonself citations: Barreira, Luís; Pesin, Yakov; Schmelling, Jorg, Dimension and product structure of hyperbolic measures, Annals of Mathematics, 149 (1999), 755–783.
  16. 101 nonself citations: Gomes, Diogo A.; Mohr, Joana; Souza, Rafael Rigão, Continuous Time Finite State Mean Field Games, Applied Mathematics and Optimization, 68 (2013), 99–143.
The numbers of highly cited articles with similar criteria with authors elsewhere in Portugal are:
8 at Faculty of Sciences and Technology of U. of Coimbra (3 with a same author, 2 others with another same author),
6 at Faculty of Sciences of U. of Lisbon (3 authored by Teresa Faria who had received MSc and PhD trainning at CAMGSD, and each one of the others with different authors),
4 at Faculty of Sciences and Technology of New U. of Lisbon (2 with each one of 2 authors),
4 at Faculty of Sciences and Technology U. of Algarve (all with a same author);
1 at Faculty of Sciences of U. of Porto (with 1 author).
As of 06.JUL.2026.
Thus, the CAMGSD contributed with 40% of such highly cited Mathematics articles, while it accounted only to about 10% of researchers in all Mathematics R&D Units in Portugal (source: FCT - Science and Technology Foundation 2024 data for PhD Integrated Members in R&D Units).