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A Volume Preserving Diffeomorphism with Essential Coexistence of Zero and Nonzero Lyapunov Exponents

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Abstract

We show that there exists a C ∞ volume preserving topologically transitive diffeomorphism of a compact smooth Riemannian manifold which is ergodic (indeed is Bernoulli) on an open and dense subset \({\mathcal{G}}\) of not full volume and has zero Lyapunov exponent on the complement of \({\mathcal{G}}\) .

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Authors and Affiliations

  1. Department of Mathematics, Michigan State University, East Lansing, MI, 48824, USA

    Huyi Hu

  2. Department of Mathematics, Pennsylvania State University, University Park, PA, 16802, USA

    Yakov Pesin

  3. Northwestern University, Evanston, USA

    Anna Talitskaya

  4. Math&more Studio, 1 Militia Dr, Suite #6, Lexington, MA, 02421, USA

    Anna Talitskaya

Authors
  1. Huyi Hu
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  2. Yakov Pesin
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  3. Anna Talitskaya
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Corresponding author

Correspondence to Yakov Pesin.

Additional information

Communicated by G. Gallavotti

H. H. was partially supported by NSF grant DMS-0503870; Ya. P. was partially supported by the NSF grant DMS-1101165.

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Hu, H., Pesin, Y. & Talitskaya, A. A Volume Preserving Diffeomorphism with Essential Coexistence of Zero and Nonzero Lyapunov Exponents. Commun. Math. Phys. 319, 331–378 (2013). https://doi.org/10.1007/s00220-012-1602-0

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  • DOI: https://doi.org/10.1007/s00220-012-1602-0

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