Terceras Jornadas de Introducción a los Sistemas Dinámicos. JISD2004

JORNADES D'INTRODUCCIÓ ALS SISTEMES DINÀMICS (JISD2004)

Barcelona, June 28- July 2, 2004

The third edition of the JORNADES D'INTRODUCCIÓ ALS SISTEMES DINÀMICS (JISD2004), will be held from June 28 to July 2, 2004 at the Universitat Politècnica de Catalunya (UPC), in Barcelona.

The JISD2004 will be devoted to the two courses

• Asymptotic Methods In Dynamical Systems (48114), by Prof. Luigi Chierchia, Università degli Studi ``Roma Tre", on the topic Quasi-periodic solutions for the three-body problem.
• Seminar of Hamiltonian Systems and Celestial mechanics (48036), by Prof. Alain Chenciner, Institut de Mécanique Céleste, Paris, on the topic Calculus of variations and introduction to weak KAM theory.

of the Doctoral Programme in Applied Mathematics, inside the Graduate studies at UPC, under the supervision of Prof. Tere M. Seara, coordinator of the Programme. The courses will be delivered from June 28 to July 2, and will consist on 5 hours lectures every day.

The JISD2004, as well as the Doctoral Programme in Applied Mathematics, is supported by a Spanish grant Mención de calidad en programas de doctorado .

Contents

Both courses will deal with K.A.M. theory and its applications.

• Luigi Chierchia, Quasi-periodic solutions for the three-body problem

  1. Hamiltonian formulation for nearly-integrable three-body problems.
  2. KAM theory.
  3. Maximal quasi-periodic solutions and total stability for the restricted, planar, circular three-body problem.
  4. An overview of extensions, perspectives and open problems.

• Alain Chenciner, Calculus of variations and introduction to weak KAM theory

  1. In a first part, the study of the variations of an action integral of the form leads to a natural introduction of the basic notions of Classical Mechanics: Legendre transform, Hamiltonian, Poincaré-Cartan integral invariant, symplectic and contact structures, Hamilton-Jacobi theory.
  2. In the second part, one restricts the attention to convex and superlinear Lagrangian, the ones for which exists a good theory of minimization, in particular Tonelli's theorem. In the ``weak KAM theory" (Fathi's terminology), one uses minimization to find global weak solutions of the Hamilton-Jacobi equation which arise in many domains of mathematics, for example, Aubry-Mather theory, viscosity solutions, etc.