Partial hyperbolicity, Lyapunov exponents and stable ergodicity

Abstract:

We present some results and open problems about stable ergodicity of partially hyperbolic diffeomorphisms with non-zero Lyapunov exponents. The main tool is local ergodicity theory for non-uniformly hyperbolic systems.

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Authors' addresses:
	Keith  Burns 
	Department of Mathematics
	Northwestern University
	Evanston, IL 60208-2730

        burns followed by math.northwestern.edu

	
        Dmitry Dolgopyat
	Department of Mathematics
	Pennsylvania State University
	University Park, PA 16802
	dolgop followed by math.psu.edu


	Yakov Pesin
	Department of Mathematics
	Pennsylvania State University
	University Park, PA 16802
	pesin followed by math.psu.edu