Seminar on Dynamical Systems: Euler International Mathematical Institute, St. Petersburg, 1991(12 Progress in Nonlinear Differential Equations and Their Applications)

The "Dynamical Systems Semester" took place at the Euler International Mathematical Institute in St. Petersburg, Russia, in the autumn of 1991. There were two workshops, October 14-25 and November 18-29, with more than 60 participants giving 70 talks. The titles of all talks are given at the end of this volume. Here we included 22 papers prepared by the authors especially for this volume, while the material of the other talks are published elsewhere. The semester was sponsored by the Soviet Academy of Sciences and UN­ ESCO. Since the new building of the Euler Institute was not ready at that moment, the sessions were held in the old building of the Steklov Mathemati­ cal Institute in the very center of St. Petersburg. Members of the staff of the Euler Institute were doing their best to organize properly the normal processing of the conference-not a simple task at that time because of the complications in the political and economical life in Russia just between the coup d'etat in August and the dismantling of the Soviet Union in December. We are thankful to all of them.

Table of Contents:
I. KAM theory and related topics.- 1. The dynamical foundation of classical statistical mechanics and the Boltzmann-Jeans conjecture.- 2. Stability of nearly integrable convex hamiltonian system over exponentially long times.- 3. On the stability problem for nearly-integrable hamiltonian systems.- 4. Separatrices splitting for the rapidly forced pendulum.- 5. Exponentially small expressions for separatrix splitting.- 6. An unusual variational problem connected with Mather’s theory for monotone twist mappings.- 7. Periodic Metrics.- 8. On the inclusion of analytic symplectic maps in analytic hamiltonian flows and its applications.- 9.Poincaré Compacti-fication of the Kepler and the collinear three body problems.- 10. A note on the existence of heteroclinic orbits in the planar three-body problem.- 11. KAM tori for modulated symplectic maps.- 12. Analyticity of normalizing transformations for area preserving maps.- 13. On the frequencies of quasi-periodic solutions of analytic nearly integrable hamiltonian systems.- 14. New results in the reversible KAM theory.- II. Infinite dimensional dynamical systems.- 15. Maximal almost periodic solutions for Lagrangian equations on infinite dimensional tori.- 16. Nonpersistence of breather solutions under perturbation of the Sine-Gordon equation.- III. Miscellanea.- 17. Attractors, integrable hamiltonian systems and the Reidemeister torsion.- 18. Linear connections for hamiltonian dynamics over isotropic submanifold.- 19. Four-dimensional integrable hamiltonian systems with simple singular points.- 20. Periodic points and Symbolic Dynamics.- 21. On the perturbation of locally non-unique invariant manifolds.- 22. Complex geometry of the billiard on the ellipsoid and quasicristallic curves.