Castellón, 24 January 2005 - 28 January 2005




 This is the second winter school in Dynamical Systems of the Spanish network DANCE (Dinámica, Atractores y Nolinealidad: Caos y Estabilidad).

This winter school will be located in the Department of Mathematics of the Universitat Jaume I, Castellón, Spain.

The goal of these winter shools is to train their participants to theory and applications in the field of nonlinear science; with the aim that theory and applications enforce each other.

This will be done in an atmosphere of informal discussion and interchange of ideas.

The idea of these winter schools is to help young researchers for their basic training and open new fields for the senior ones.

These courses have received official recognition in the doctorate programs of Universitat Autònoma de Barcelona and Universitat Politècnica de Catalunya.




Lluís Alsedà (Universitat Autònoma de Barcelona)
Amadeu Delshams (Universitat Politècnica de Catalunya)


Fernando Casas (Universitat Jaume I)
Bartomeu Coll (Universitat de les Illes Balears)
Emilio Freire (Universidad de Sevilla)
Jaume Llibre (Universitat Autònoma de Barcelona)
José Martínez Alfaro (Universitat de València)


Sergio Blanes (Universitat Jaume I)
Beatriz Campos (Universitat Jaume I)
Cristina Chiralt (Universitat Jaume I)
Alicia Cordero (Universitat Politècnica de València)
Pura Vindel (Universitat Jaume I) [Webmaster]

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Scientific Sessions

 Distortion in Lattice Actions on Surfaces - John Franks (Nortwestern University)


In these lectures we consider how algebraic properties of discrete subgroups of Lie groups restrict the possible actions of those groups on surfaces. The results show a strong parallel between the possible actions of such a group on the circle S1 and the measure preserving actions on surfaces.

Our aim is the study of the (non)-existence of actions of lattices in a large class of non-compact Lie groups on surfaces. A definitive analysis of the analogous question for actions on S1 was carried out by É. Ghys. Our approach is topological and insofar as possible we try to isolate properties of a group which provide the tools necessary for our analysis. The two key properties we consider are almost simplicity and the existence of a distortion element. Both will be defined and described in the lectures.

Our techniques are almost all from low dimensional dynamics. But we are interested in how algebraic properties of a group, commutativity, nilpotence, etc. affect the possible kinds of dynamics which can occur. For most of the results we will consider groups of diffeomorphisms which preserve an Borel probability measure.

 Numerical methods for invariant objects - Àngel Jorba (Universitat de Barcelona)


The main goal is to show how the numerical approximation of invariant objects can be used to study a given dynamical system.

In the course we will first focus on several concrete problems and we will show how the computation of invariant manifolds appear as a natural tool to understand the geometry of phase space. Then, we will introduce several numerical tools and we will discuss how to implement them in a computer. Finally, the results will be used to describe the considered phenomena.

The examples come from Hamiltonian dynamics, celestial mechanics, dissipative low dimensional systems and PDEs. The considered tools are the analysis of bifurcations, the computation of invariant manifolds (invariant tori, stable and unstable manifolds, etc.) and the estimation of Lyapunov exponents.

 Lyapunov exponents - Marcelo Viana (IMPA)


Interval exchange transformations have been a continuous source of beautiful questions (and beautiful answers), not the least because they relate very closely to many other topics, such as poligonal billiards, measured foliations, Teichmuller geodesic flows, flat surfaces, renormalization theory, continued fraction expansions, and yet many others.

The Zorich-Kontsevich conjecture, formulated in the mid- nineties, proposes a surprisingly detailed description of the behavior of typical interval exchange transformations in terms of an "asymptoctic flag". The conjecture was recently proved by Avila and myself, and the proof also contains very important partial progress obtained a couple of years ago by Forni.

The course will be a self contained introduction to this field, meant to convey the flavor of the main objects and their relationships, as well as some outline of the proof of the conjecture.

 John Franks (Nortwestern University. Illinois. USA)
 Marcelo Viana (IMPA)
 Frederic Gabern (Universitat de Barcelona)
 Àngel Jorba (Universitat de Barcelona)
 Àngel Jorba (Universitat de Barcelona)
 Àngel Jorba (Universitat de Barcelona)
 Àngel Jorba (Universitat de Barcelona)
 Primitivo B Acosta Humánez, Universitat Politècnica de Catalunya (Spain)
 Begoña Alarcón Cotillas, Universitat de València (Spain)
 Ana Isabel Alonso, Universidad de Valladolid (Spain)
 Manuel Alonso Morón, Universidad Complutense de Madrid (Spain)
 Lluis Alsedà, Universitat Autònoma de Barcelona (Spain)
 Martha Álvarez Ramírez, Universidad Autónoma de México (Mexico)
 Alejo Barrio Blaya, Universidad de Murcia (Spain)
 Sergio Blanes Zamora, Universitat Jaume I (Spain)
 David Blázquez Sanz, Universitat de Barcelona (Spain)
 Julien Bodossian, ASD IMCCE Observatoire de Paris (France)
 Renato Calleja, University of Texas at Austin (USA)
 Beatriz Campos Sancho, Universitat Jaume I (Spain)
 Elisabet Canalias Vila, Universitat Politècnica de Catalunya (Spain)
 Pablo S. Casas, Universitat Politècnica de Catalunya (Spain)
 Fernando Casas, Universitat Jaume I (Spain)
 Alicia Cordero Barbero, Universidad Politécnica de Valencia (Spain)
 Sara Costa Romero, Universitat Autònoma de Barcelona (Spain)
 Georgios Chatzivantsidis, Aristotle University of Thessaloniki (Greece)
 Cristina Chiralt Monleón, Universitat Jaume I (Spain)
 Lauand R. Darbas Barbé, Universitat Politècnica de Catalunya (Spain)
 Joaquín Delgado, Universidad Autónoma de México (Mexico)
 Amadeu Delshams, Universitat Politècnica de Catalunya (Spain)
 Fátima Drubi Vega, Universitat Autònoma de Barcelona (Spain)
 Antonio Falcó Montesinos, Universidad Cardenal Herrera de Elche (Spain)
 Ariadna Farrés Basiana, Universitat de Barcelona (Spain)
 John Franks, Northwestern University (USA)
 Frederic Gabern, Universitat de Barcelona (Spain)
 Victoria Galiot Torronteras, Universitat de Barcelona (Spain)
 Claudio Gomes Pessoa, Universitat Autònoma de Barcelona (Brasil)
 Marina S Gonchenko, Nizhny Novgorod State University (Russia)
 Gemma Huguet Casades, Universitat Politècnica de Catalunya (Spain)
 Guillem Huguet Serra, Universidad Pública de Navarra (Spain)
 Xavier Jarque, Universitat de Barcelona (Spain)
 Àngel Jorba, Universitat de Barcelona (Spain)
 Henrik Kalisch, NTNU Trondheim (Norway)
 Paul L. Larsen, University of Texas at Austin (USA)
 Tomás Lázaro, Universitat Politècnica de Catalunya (Spain)
 Alejandro Luque Jiménez, Universitat Politècnica de Catalunya (Spain)
 Adam Mahdi, Universitat Autònoma de Barcelona (Poland)
 Josep Maria Mondelo González, Universitat Autònoma de Barcelona (Spain)
 Fco. Javier Muñoz Almaraz, Universitat de Barcelona (Spain)
 Montserrat Navarro Tapias-Fernando, Universitat de Barcelona (Spain)
 Carmen Núñez, Universidad de Valladolid (Spain)
 Carme Olivè, Universitat Rovira i Virgili (Spain)
 I. Ovsyannikov, Nizhny Novgorod State University (Russia)
 Chara Pantazi, Universitat Politècnica de Catalunya (Spain)
 Alfred Peris, Universidad Politécnica de Valencia (Spain)
 Benito F Pires, Universitat Autònoma de Barcelona (Spain)
 Iván Remizov, Nizhny Novgorod State University (Russia)
 Pau Roldán González, Universitat Politècnica de Catalunya (Spain)
 Mercè Romero Gómez, Universitat Rovira i Virgili (Spain)
 David Romero Sánchez, Universitat Autònoma de Barcelona (Spain)
 Francisco Ruiz del Portal, Universidad Complutense de Madrid (Spain)
 J. Manuel Salazar Crespo, Universidad de Alcalá (Spain)
 Anna Samà, Universitat Autònoma de Barcelona (Spain)
 Jaime Jorge Sánchez Gabites, Universidad Complutense de Madrid (Spain)
 Emil Sekula, Universitat Politècnica de Catalunya (Spain)
 Vesna Stojanoska, American University in Bulgaria (Bulgaria)
 Joan Carles Tatjer Montaña, Universitat de Barcelona (Spain)
 Antonio E. Teruel Aguilar, Universitat de les Illes Balears (Spain)
 Miguel Toledo González, Universitat Politècnica de Catalunya (Spain)
 Joan Torregrosa Arús, Universitat Autònoma de Barcelona (Spain)
 Saverio Trioni, Universitat Autònoma de Barcelona (Spain)
 Sergei Utkin, Nizhny Novgorod State University (Russia)
 Tonatihu Valdéz Hernández, Universitat Autònoma de Barcelona (Spain)
 Marcelo Viana, IMPA - Instituto Nacional de Matemática Pura e Aplicada (Brasil)
 Arturo Vieiro Yanes, Universitat de Barcelona (Spain)
 Jordi Villanueva, Universitat Politècnica de Catalunya (Spain)
 Pura Vindel, Universitat Jaume I (Spain)