Hyperbolicity in Dynamics on Compact and Non-Compact Manifolds

Resumen:

The notion of hyperbolicity is central to the modern theory of dynamics.  I would like to quickly review the idea of hyperbolicity for a fixed or periodic point, and the accompanying structure of stable and unstable manifolds, then see how these extend to a global notion of hyperbolic behavior on a compact invariant set, especially when the set is the entire phase space of the system (Anosov diffeomorphisms).  Then I would like to discuss the subtle way in which these concepts change when the underlying space is not compact, discussing some joint work with Jorge Groisman concerning “Anosov” diffeomorphisms in the plane.

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