Carles SIMO

Departament de Matemàtica Aplicada i Anàlisi
Universitat de Barcelona
Gran Via de les Cortes catalanes, 585
08007 Barcelona
Espagne
carles@maia.ub.es

Geometry of Hamiltonian Dynamics: Goals and Methods

Abstract : Hamiltonian Dynamics appears in a natural way in many physical problems. In this talk we shall present a quick review dealing with the following topics: \begin{itemize}

\item[-] The geometrical objects in the phase space: fixed points, periodic orbits, invariant tori. Hyperbolicity and the related invariant manifolds. Homoclinic phenomena.

\item[-] Dynamical consequences: Integrability, stability and practical stability, capture and escape, diffusion, chaos. Their detection.

\item[-] The tools: Algebraic, analytical, variational, topological, probabilistical, symbolical, numerical, graphical.

\item[-] Applications: Variants of the two body problem, the three body problem, geodesics, billiards, etc.

\item[-] Extensions: Limit PDE, volume preserving flows, etc.

\end{itemize}