On the Work of Dolgopyat on Partial and Nonuniform Hyperbolicity
نویسنده
چکیده
The paper is a non-technical survey and is aimed to illustrate Dolgopyat’s profound contributions to smooth ergodic theory. I will discuss some of Dolgopyat’s work on partial hyperbolicity and nonuniform hyperbolicity with emphasis on interaction between the two – the class of dynamical systems with mixed hyperbolicity. On the one hand, this includes uniformly partially hyperbolic diffeomorphisms with nonzero Lyapunov exponents in the center direction. The study of their ergodic properties has provided an alternative approach to Pugh-Shub stable ergodicity theory for both conservative and dissipative systems. On the other hand, ideas of mixed hyperbolicity have been used in constructing volume preserving diffeomorphisms with nonzero Lyapunov exponents on any manifolds.
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Partial Hyperbolicity, Lyapunov Exponents and Stable Ergodicity
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