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

2006/06/28 by Sébastien Gouëzel, Carlangelo Liverani, Gouezel, Sebastien +1 · 4 citations
Mathematics · #Mathematical Dynamics and Fractals #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.math/0606722

Abstract

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.

Citations

• Markov extensions, zeta functions, and Fredholm theory for piecewise invertible dynamical systems

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