Ergodic optimization theory for Axiom A flows

Wen Huang; Zeng Lian; Xiao Ma; Leiye Xu; Yiwei Zhang

Ergodic optimization theory for Axiom A flows

Dynamical Systems 2019-09-04 v2

Authors: Wen Huang , Zeng Lian , Xiao Ma , Leiye Xu , Yiwei Zhang

Abstract

In this article, we consider the weighted ergodic optimization problem Axiom A attractors of a $C^2$ flow on a compact smooth manifold. The main result obtained in this paper is that for a generic observable from function space $\mc C^{0,\a}$ ( $\a\in(0,1]$ ) or $\mc C^1$ the minimizing measure is unique and is supported on a periodic orbit.

Keywords

geodesic flow ergodic theory anosov flows

Cite

@article{arxiv.1904.10608,
  title  = {Ergodic optimization theory for Axiom A flows},
  author = {Wen Huang and Zeng Lian and Xiao Ma and Leiye Xu and Yiwei Zhang},
  journal= {arXiv preprint arXiv:1904.10608},
  year   = {2019}
}

Comments

49 pages

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