Dynamical Systems and Differential Equations

 

Dynamical Systems can be considered, at present, as a way to describe evolution problems with respect to time, let them be given by ordinary or partial differential equations or by discrete transformations. Both the qualitative and the quantitative aspects of the systems fall in this study. A key idea is the consideration of that evolution in the phase space or, better, in the phase-and-parameter space, to take into account the dependence of the system with respect to parameters (bifurcations).

Dynamical Systems interacts with many areas of mathematics such as algebra, geometry, topology, number theory, analysis, probability, statistics, combinatorics, algorithmics, etc. Their applications reach all areas of  science and technology.

This area  has a long tradition in Barcelona. There are groups in every BGSMath unit working in different aspects of Dynamical Systems, including theory, computation and applications.

Research Lines

Celestial Mechanics and Astrodynamics

Keywords: Invariant tori. N-body problem. Central configurations. Space mission design. Station keeping.

Amadeu Delshams (UPC)
Gerard Gómez (UB)
Àngel Jorba (UB)
Jaume Llibre (UAB)
Josep Maria Mondelo (UAB)
Mercè Ollé (UPC)
Carles Simó (UB)

 

Differentiable and Hamiltonian Dynamics

Key words: Invariant manifolds. KAM theory. Diffusion and Arnold diffusion. Integrability. Exponentially small phenomena. Billiard systems. Reversible systems. Mathematical and computational neuroscience.

Immaculada Baldomà (UPC)
Ernest Fontich (UB)
Joan Carles Tatjer (UB)
Amadeu Delshams (UPC)
Marcel Guàrdia (UPC)
Antoni Guillamon (UPC)
Gemma Huguet (UPC)
Alex Haro (UB)
Àngel Jorba (UB)
Tomás Lázaro (UPC)
Pau Martín (UPC)
Tere Martínez-Seara (UPC)
Juan Ramón Pacha (UPC)
Carles Simó (UB)
Arturo Vieiro (UB)

Nonsmooth Dynamics and Control Theory

Keywords: Piecewise linear systems. Filippov systems. Sliding mode control. Energy-based control. Geometric control. Complex networks.

Carles Batlle (UPC)
Jaume Franch (UPC)
Jaume Llibre (UAB)
Teresa Martínez-Seara (UPC)
Josep Maria Olm (UPC)
Jordi Riera (UPC)
Joan Torregrosa (UAB)

Qualitative Theory of Vector Fields

Keywords: The 16th Hilbert problem. Period function and isochronicity. Global asymptotic stability and Jacobian Conjecture. Averaging theory.
Magdalena Caubergh (UAB)
Anna Cima (UAB)
Armengol Gasull (UAB)
Jaume Llibre (UAB)
Francesc Mañosas (UAB)
Joan Torregrosa (UAB)

Low Dimensional Discrete Dynamics (Real and Complex)

Key words: Dynamics on graphs. Topological and metric entropy. Ergodic Theory. Quasi periodic skew products. Strange attractors Holomorphic dynamics. Julia and Fatou sets. Transcendental dynamics.

Lluís Alsedà (UAB)
Anna Cima (UAB)
Núria Fagella (UB)
Armengol Gasull (UAB)
Alex Haro (UB)
Xavier Jarque (UB)
Àngel Jorba (UB)
Jaume Llibre (UAB)
Francesc Mañosas (UAB)
Pau Martin (UPC)
Carles Simó (UB)
Joan Carles Tatjer (UB)
Arturo Vieiro (UB)

 

Links to research groups

Researchers in the Barcelona area, and more generally in Catalonia, group themselves into smaller research groups, following not only academic but also administrative criteria, like location or research grants.