Dynamical systems theory looks for the milestones that organize dynamics, essentially their invariant objects and their connections. In this ambitious goal, the group has a recognized track record and a leading role, addressing it through, among others, analytical, geometrical, topological, or numerical tools, which, complemented, also contribute to a deeper understanding of the dynamics of a system. The dynamics of the systems studied, which are real or complex, can be both discrete and continuous, their dimensions are low or high, depending very much on the specific applications.
In low-dimensional systems, the search for periodic orbits and their repercussions on global dynamics is of paramount importance, especially as a result of the associated symbolic, topological, and combinatorial dynamics. The computational and numerical implementation for looking the phase portraits and bifurcation diagrams is also widely used in modelization and other applications.
In high-dimensional systems, the search for invariant tori and their disposition into normally hyperbolic invariant objects is studied especially to describe the skeleton from which emanates global dynamics, such as KAM theory, Arnold diffusion, and associated exponentially small phenomena, with special attention to applications in Celestial Mechanics, Astrodynamics, Neuroscience, and Chemistry.
I am a PH. D. in Mathematics since 1984 and professor at the Universitat Autònoma de Barcelona since 2004. Previously I have occupied a number of permanent positions in Mathematics and Economics.
Principal Investigator of 5 research grants of the Discrete Dynamical systems Group of the UAB from the Spanish Ministry of Science, as well as other specific projects.
I have supervised 8 PhD Thesis and a number of master thesis. I have published 1 book (two editions) and 4 books as associate editor. Also I have 93 published papers.
I have been Vice-Dean for Studies of the Faculty of Economics of the UAB, Director of the Department of Mathematics of the UAB, member of the Scientific Committees of several societies, main organizer of several international conferences with associated grants and I have been evaluating projects for several research agencies. Also, I have been co-creator and co-cordinator (during two terms of three years) of the Spanish network DANCE (dance-net.org; including 220 researchers on dynamical systems and non-linear dynamics of the whole Spain).
I am a member of the Governing Board of the Barcelona Graduate School of Mathematics since 2013, a member of the Jury of the annual price Ferran Sunyer i Balaguer and Associate Editor of DCDS-A and JDEA.
Associate Professor at UPC. In addition I hold two position as the Academic Secretary of the Executive Committee of the Catalan Mathematical Society (in catalan, Junta directiva de la Societat Catalana de Matemàtiques (SCM) de Matemàtiques (SCM) and I am A member of the Directive Board of the Department of Mathematics of the UPC: Vicechair of Research (in catalan, Sotsdirectora de Recerca del Departament de Matemàtiques de la UPC).
Jezabel Curbelo is a Ramon y Cajal Research Fellow at Universitat Politècnica de Catalunya. She has previously held positions at various universities, including the Department of Atmospheric and Oceanic Sciences at UCLA and the Laboratoire de Géologie de Lyon. Her PhD thesis (Universidad Autónoma de Madrid, 2014) was awarded with the “2015 Donald L. Turcotte Award” (American Geophysical Union). She has received several awards for her research in geophysical fluid dynamics including the ”Leonardo Fellowships 2022” (BBVA Foundation) and the ”2021 L’Oréal-UNESCO For Women in Science” award (L’Oréal Spain).
I am a member of the Editorial Board of several Journals: Discrete and Continuous Dynamical Systems, Gaceta de la RSME, Journal of Nonlinear Science, Journal of Differential Equations, Qualitative Theory of Dynamical Systems.
I am/was involved in organizing several events: the CRM Research Program SIMS08, the AIMS Conferences, the first Iberian Mathematical Meeting, the Carles Simó Fest, the DANCE meetings Ddays, the Spanish meetings Nolineal, the DANCE Winter Schools RTNS, the Workshops of Interaction between Dynamical Systems and PDE JISD, as well as other events of our group.
I have been Invited speaker in a number of conferences, like the 6th European Congress of Mathematics, Krakow, 2012, SIAM DSPDES’s, Barcelona, 2010, etc.
I am currently a member of the Laboratory of Geometry and Dynamical Systems at UPC-EPSEB.
Kostiantyn Drach works in the fields of dynamical systems, geometric inequalities, and topological data analysis. He is currently a postdoc at the Institute of Science and Technology Austria. Starting in September, Kostya will be an assistant professor at the Universitat de Barcelona in Spain.
Kostya is a native of Kharkiv. After graduating from the Kharkiv Physics and Mathematics Lyceum No. 27, he obtained his bachelor’s, master’s, and doctoral degrees from the V. N. Karazin Kharkiv National University, earning many distinctions on the way.
I received my Ph.D. in 1995 from Boston University under the supervision of Robert L. Devaney. I am now a full professor at Universitat de Barcelona and the co-leader of the research group Holodyn, working in complex dynamical systems. I was awarded an Icrea Academia award in 2021 and a Chern Professorship at MSRI (Berkeley) in 2022. I supervised five Ph.D. students and several postdoctoral fellows. Jointly with Bodil Branner (DTU Denmark) I am the author of the book “Quasiconformal Surgery in Holomorphic Dynamics”, Cambridge University Press (2014). I have published over 50 papers in leading journals including Inventiones Mathematicae, Advances in Mathematics or Transactions of the AMS.
I received my PhD in 1985 from Universitat de Barcelona under the supervision of Prof. Carles Simó. I was awarded the Ferran Sunyer Balaguer price in 1987 for my PhD thesis. From 1979 to 1989 I was assistant professor and associate professor at Universitat Politècnica de Catalunya. In 1989 I moved to Universitat de Barcelona, where I am professor since 2006. From 2007-2011 I was the director of the former Departament de Matemàtica Aplicada i Anàlisi (UB).
My main interest is the understanding of the global behaviour of dynamical systems. I have been working on differential equations (autonomous or not) and on discrete dynamical systems, with special emphasis on difference equations. In my research, apart from the general theory of dynamical systems, I use techniques of analysis, geometry, algebra, algebraic geometry, numerical analysis and simulation.
I have published more than 100 papers collaborating with 45 researches around the world. Together with some of them I have solved several conjectures: the Markus-Yamabe Conjecture about global asymptotic stability of differential equations, open since 1960; the Composition Conjecture appearing in the study of Abel equations; and a conjecture of E. C. Zeeman about the existence of rational 9-periodic points for the Lyness recurrence. I also have contributed to the qualitative theory of planar differential equations, with my results on the number of limit cycles and the period function.
Recently, my joint paper, A. Cima, A. Gasull and V. Mañosas, Basin of attraction of triangular maps with applications, has received the prize to the best paper published in Journal of Difference Equations and its Applications during 2014.
Marcel Guàrdia is Associate Professor at the Universitat de Barcelona and affiliated at the Centre de Recerca Matemàtica. He is the Principal Investigator of the ERC Starting grant Haminstab and he has been distinguished with an ICREA Academia Prize in 2018. He is also the Scientific Director of the Maria de Maeztu award of the Centre de Recerca Matemàtica.
His research is (mostly) focused on the analysis of invariant objects and unstable behaviors in Hamiltonian systems of finite or infinite dimension (including Partial Differential Equations) and its applications to Celestial Mechanics.
Àlex Haro is an assistant professor at the Departament de Matemàtiques i Informàtica de la Universitat de Barcelona (UB), where he is the coordinator of the PhD program in Mathematics and Computer Science.
He did his thesis (October 1998) under the supervision of professor Carles Simó. Funded by the Fulbright program, he did a postdoctoral stay at the University of Texas at Austin, where he started a fruitful collaboration with professor Rafael de la Llave, now at Georgia Institute of Technology (Atlanta). He got a permanent position at UB in July 2001. He was a member of the program “Hamiltonian systems, from topology to applications through analysis” at MSRI (Berkeley), during the second half of 2018.
His work with Jordi-Lluís Figueras and Alejandro Luque on computer-assisted proofs in KAM theory was awarded two international prizes: The Barcelona Dynamical Systems Prize (2017) and the R.E. Moore Prize for Applications of Interval Analysis (2018).
Dr. Xavier Jarque is a professor at Universitat de Barcelona (UB), which he joined in 2003 (on leave at Universitat Rovira i Virgili, Tarragona, from 2008 to 2010). Hi did the Pd.D. at Universitat Autònoma de Barcelona and he spent two years at Boston University (Boston, MA) as post-doctoral fellowship. As a researcher he has focussed in holomorphic dynamics, more concretly in transcendental dynamics as discrete dynamical systems genereted by the iterates of transcendental meromorphic maps. He is member of the research group HOLODYN (http://www.maia.ub.es/holodyn/) and GSD-UAB (http://www.gsd.uab.cat/). Since 2003 has had taught, among other subjects, Differential Equations, Dynamical Systems and Numerical Analysis. During the last 10 years he had taught (joint with Ernest Fontich) the Dynamical Systems course at the Master in Advanced Mathematics. Further information at: http://www.maia.ub.es/~xjarque
Dr. en Matemàtiques per la UB l’any 1991. Ha estat professor a la UPC i des de 1997 és Catedràtic de Matemàtica Aplicada a la UB. Pertany al Comitè Editorial (des de 2001) de “Discrete and Continuous Dynamical Systems – Series B”, i ha estat coordinador de la xarxa espanyola de sistemes dinàmics DANCE, des de 2006 fins al 2010. La seva tasca investigadora inclou la Mecànica Celeste i l’Astrodinàmica, amb èmfasi en el disseny de missions espacials. També ha treballat en l’existència de moviments quasi-periòdics en sistemes dinàmics, i en el desenvolupament d’eines numèriques i semi-analítiques per aplicar la teoria de sistemes dinàmics a situacions reals.
Former assistent professor at UPC.
Current position: associate professor at UPC.
- Dynamical Systems
- Models in Biology
- Reversible systems
- Singular perturbation theory
- Hilbert’s 16th problem
- Differential Galois Theory
Early works, under the supervision of Ernest Fontich, dealt about the problem of abundance of Arnold difussion in the context of analytic Hamiltonian systems. Besides proving the density of systems with exhibiting such behaviour, several tools were developed that have been used afterwards by several authors.
Related to the problem of instability, the splitting of separatrices has also been studied, both for area preserving maps and Hamiltonian systems of higher dimension.
As a consequence of these last developments, recently a prove has been found of the existence of oscillatory motions in the restricted planar circular three body problem for all values of the mass paramenter, closing a long standing problem.
Tere Martínez Seara
Tere M-Seara is full professor at the Dpt. de matemàtiques of the Universitat Politècnica de Catalunya. She is the leader of the UPC Dynamical Systems group, formed by more than 20 researchers working on theoretical and computer aspects of finite and infinite Dynamical Systems, with focus on Celestial Mechanics and mathematical Neuroscience. She has supervised 8 PhD. students. In 2015, she received the first Barcelona Dynamical Systems Prize and in the fall of 2018 she hold an Eisenbud Professorship (Simons Foundation) at MSRI (U. Berkeley).
She belongs to the editorial board of Nonlinearity, SIADS, NOdea; SEMA-SIMAI Springer series and has published about 60 papers including articles in the journals: Adv. Math., Comm. Math. Phys, Comm. Pure and Applied Math., Inventiones Mathematicae, J. of Differential Equations, J. of Nonlinear Science, Memoirs of the A.M.S.
Tere M-Seara works in Dynamical Systems, in analytical tools to study their global dynamics.
Her works developed two tools which have been widely used in the area of Arnold Diffusion: the study of normally hyperbolic invariant manifolds and the theory of the “scatering map”.
She also works in a rigourous approach to singular perturbation theory: developing methods which allow to measure exponentially small phenomena which are relevant in the study of the global dynamics of a system like the exponentially small splitting of separatrices, one of the main phenomena producing chaos.
Professor at the Department of Mathematics of the University Politècnica de Catalunya, PhD Thesis in 1989 (supervised by Prof. Gerard Gomez), member of the UPC-UB Dynamical Systems Group (a large group of researchers in DS based in Barcelona), and the DANCE network. Advisor of two PhD Theses and 30 published papers in JCR, 21 in Q1 (10 of them in D1, one of them as unique author), 8 in Q2, 1 in Q3, (info up today 31 January 2022). Distinction: The paper Dynamics of the parabolic restricted three-body problem, in Comm. Nonlinear Sci. Numer. Simulat., 29,400-415, 2015, was selected by Elsevier in the Virtual Special Issue on Women in Physics, March, 8, 2016.
After my PhD in UAB I worked for two years in Universitat de les Illes Balears as Associate Professor (2000-2001). In 2009 I had the award “I3 Intensification young researchers DIUE-MEC 2007 (2009-2011)”. I have the “Acreditation of Advanced Research Position” by AQU-Catalunya and the “Full Professor Acreditation” by ANECA”. Coordinator of the Spanish Dynamical Systems Network from 2018. PI of some Spanish research projects from 2014.
I am currently an associate professor at UB.
My PhD was awarded with the
Some of my papers have been selected as highlight
I co-advised the PhD thesis:
Mı́guel-Baños, N. “Transport phenomena and anomalous diffusion in conservative systems of low dimension”. Universitat de Barcelona, 2016. Co-advised with C. Simó. Dipòsit Digital UB: http://diposit.ub.edu/dspace/handle/2445/107215