Compact locally maximal hyperbolic sets for smooth maps: fine statistical properties

Sébastien Gouëzel (1) , Carlangelo Liverani (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 DIPMAT - Dipartimento di Matematica [Roma II]

Compact locally maximal hyperbolic sets are studied via geometrically defined functional spaces that take advantage of the smoothness of the map in a neighborhood of the hyperbolic set. This provides a self-contained theory that not only reproduces all the known classical results but gives also new insights on the statistical properties of these systems.

Mots clés: locally maximal hyperbolic sets; Ruelle resonances; Transfer Operator; statistical stability

Domaines: Systèmes dynamiques [math.DS]

Sébastien Gouëzel, Carlangelo Liverani. Compact locally maximal hyperbolic sets for smooth maps: fine statistical properties. Journal of Differential Geometry, 2008, 79 (3), pp.433-477. ⟨hal-00082731⟩