by Àngel Jorba, University of Barcelona

The Dynamical Systems group in Barcelona is mainly distributed over three Universities, Universitat Autònoma de Barcelona, Universitat de Barcelona and Universitat Politècnica de Catalunya, although some members are located at other different universities in Spain. The group was started by Carles Simó and now involves about 50 researchers and 20 PhD students.

The researchers work in smaller groups, according to scientific and/or geographical conveniences. These groups are mainly funded by the Spanish government, the Catalan goverment, and the European Union.

Members of the research group at UAB From left to right: Lluís Alsedà, Jaume Llibre and Armengol Gasull

The UAB Dynamical Systems Group is located at the Department of Mathematics of the Universitat Autònoma de Barcelona. The main areas of research are differential equations on the plane, discrete low dimensional dynamical systems, celestial mechanics and complex dynamics. The researchers are supported by several grants, whose Principal Investigators are Lluís Alsedà and Jaume Llibre.

The UB-UPC Dynamical Systems Group is mainly formed between Universitat de Barcelona and Universitat Politècnica de Catalunya (see also the webpage of the Politècnica's subgroup). The main areas of research are conservative and dissipative systems (discrete and continuous, including numerical methods), celestial mechanics and astrodynamics. The researchers are supported by several grants, whose Principal Investigators are Amadeu Delshams, Àngel Jorba and Carles Simó.

Members of the research group at UB From left to right: Manuel Marcote, Estrella Olmedo, Arturo Vieiro, Joan Carles Tatjer, Pere Mumbrú, Àlex Haro, Carles Simó, Gerard Gómez, Joaquim Font, Inma Baldomá, Ernest Fontich, Joaquim Puig and Àngel Jorba.

Activities

The preprints and publications can be found online for UAB, UB and UPC. Presently, members of the group are involved in the organization of the following events:

• Summer Course, Advanced Topics in Astrodynamics, Barcelona, July 5-10, 2004.
• 3rd School, Introduction to Dynamical Systems, Barcelona, June 28-July 3, 2004.
• Nolineal 2004, Toledo, June 1-4, 2004.

The group is also involved in the following projects:

• Mathematical Physics Electronic Journal (MPEJ). This is a refereed, completely electronic, journal on Mathematical Physics. Anyone connected to the Internet can access and/or subscribe to the full journal or just the abstracts for free. The journal was started in the University of Texas at Austin, and now is completely based in Barcelona.
• Spanish Network on Nonlinear Dynamics. The network was started by members of our group (Lluís Alsedà and Amadeu Delshams).
• Non Linear Science Network (NLS-NET). It provides a free service to the community of non linear systems, by distributing to its subscribers e-mail updates on tables of contents of several international journals, announcements of meetings, new books or journals, available positions, software, etc. related to non linear dynamical systems and its applications to any field of science. NLS-NET was created jointly with the American Institute of Mathematical Sciences (AIMS).

We have also organized (or we have been involved in the organization of) the following events:

• Winter School, Recent Trends in Nonlinear Science, Palma de Mallorca, February 2-6, 2004.
• Summer School, Nonlinear Phenomena in Computational Chemical Physics, Barcelona, June 9-14, 2003.
• Dinámica nolineal en dimensión baja y atractores extraños, Salou, March 13-15, 2003.
• Conference COM & COM, Barcelona, May 14-17, 2003.
• Conference on Libration Point Orbits and Applications, Girona, June 10-14, 2002.

Older events can be found in the web pages of the groups.

Members of the research group at UPC Back row from left to right: Elisabet Canalias, Gemma Huguet, Jordi Villanueva, Amadeu Delshams, Mercè Ollé and Pere Gutiérrez. Front row from left to right: Pau Martín, Rafael Ramírez-Ros and Toni Guillamon.

Computing facilities

One of the characteristics of the UB-UPC group is their interest in effective numerical computations in Dynamical Systems. This not only includes direct numerical simulation, but also the computation of invariant objects (periodic orbits, invariant tori, etc), their evolution and bifurcations in the parameter space, as well as their stable and unstable manifolds and related homoclinic and heteroclinic phenomena. To cope with the numerical necessities, the group has built its own clusters, namely Hidra and Eixam. The first versions were built during the fall of 1997 (Hidra) and at the beginning of 2001 (Eixam).

The current (March 2004) version of Hidra has a theoretical peak of 375 Gigaflops. Although it has delivered 250 Gigaflops in very specific applications, the usual performance in our applications is about 125 Gigaflops. Eixam still has its initial configuration (its theoretical peak is of 14 Gigaflops and the usual performance is about 4 Gigaflops). We expect that Eixam will soon be updated.