Journal of Modern Dynamics (JMD)

Center Lyapunov exponents in partially hyperbolic dynamics

Pages: 549 - 576, Issue 3/4, September/December 2014      doi:10.3934/jmd.2014.8.549

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Andrey Gogolev - Department of Mathematical Sciences, Binghamton University, P. O. Box 6000, Binghamton, NY 13902, United States (email)
Ali Tahzibi - Departamento de Matemática, ICMC-USP São Carlos, Caixa Postal 668, 13560-970 São Carlos-SP, Brazil (email)

Abstract: In this survey, we discuss the problem of removing zero Lyapunov exponents of smooth invariant measures along the center direction of a partially hyperbolic diffeomorphism and various related questions. In particular, we discuss disintegration of a smooth invariant measure along the center foliation. We also simplify the proofs of some known results and include new questions and conjectures.

Keywords:  Center Lyapunov exponent, partially hyperbolic, Pesin manifold.
Mathematics Subject Classification:  Primary: 37D25; Secondary: 37D30, 37D35.

Received: October 2013;      Revised: June 2014;      Available Online: April 2015.