Colloque des sciences mathématiques du Québec

4 janvier 2008 de 16 h 00 à 18 h 00 (heure de Montréal/HNE) Sur place

Attractors and invariant measures in low-dimensional dynamical systems

Colloque par Michael Jakobson (University of Maryland)

We consider typical behavior of trajectories in dynamical systems from topological and measure theoretical prospectives. They coincide for uniformly hyperbolic systems, but can be different for non-uniformly hyperbolic ones. Sinai-Ruelle-Bowen (SRB) measures are crucial for understanding ergodic properties of dynamical systems. In the case when a system has an absolutely continuous SRB measure its typical trajectories exhibit random behavior and at the same time their statistical properties can be described quantitatively. We discuss several types of dynamics which arise in one-parameter families of low-dimensional dynamical systems.


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