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Center Lyapunov exponents in partially hyperbolic dynamics

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  • 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.
    Mathematics Subject Classification: Primary: 37D25; Secondary: 37D30, 37D35.


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