Exponential mixing for generic volume-preserving Anosov flows in dimension three

Masato Tsujii

Exponential mixing for generic volume-preserving Anosov flows in dimension three

Dynamical Systems 2017-09-05 v5

Authors: Masato Tsujii

Abstract

Let $M$ be a closed $3$ -dimensional Riemann manifold and let $3\le r\le \infty$ . We prove that there exists an open dense subset in the space of $C^r$ volume-preserving Anosov flows on $M$ such that all the flows in it are exponentially mixing.

Keywords

Anosov flow volume-preserving exponential mixing three-dimensional manifold generic property open dense subset dynamical systems

Cite

@article{arxiv.1601.00063,
  title  = {Exponential mixing for generic volume-preserving Anosov flows in dimension three},
  author = {Masato Tsujii},
  journal= {arXiv preprint arXiv:1601.00063},
  year   = {2017}
}

Comments

52 pages, 1 figure. A few errors in the previous version are corrected. Especially we fix errors in Section 4-6 that are caused by confusion between the non-conformal linear map \mathbf{\Delta}_j and scalar multiplication by \Delta_j. Also we modified the Definition 6.14 to resolve a small error in Lemma 6.6. Besides we give more details of the argument and fix several minor errors and typos

Exponential mixing for generic volume-preserving Anosov flows in dimension three

Abstract

Keywords

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