On $\mathrm{C}^1$-class local diffeomorphisms whose periodic points are nonuniformly expanding

Xiongping Dai

On $\mathrm{C}^1$-class local diffeomorphisms whose periodic points are nonuniformly expanding

Dynamical Systems 2012-06-12 v1

Authors: Xiongping Dai

Abstract

Using a sifting-shadowing combination, we prove in this paper that an arbitrary $\mathrm{C}^1$ -class local diffeomorphism $f$ of a closed manifold $M^n$ is uniformly expanding on the closure $\mathrm{Cl}_{M^n}(\mathrm{Per}(f))$ of its periodic point set $\mathrm{Per}(f)$ , if it is nonuniformly expanding on $\mathrm{Per}(f)$ .

Keywords

diffeomorphism groups

Cite

@article{arxiv.1206.2113,
  title  = {On $\mathrm{C}^1$-class local diffeomorphisms whose periodic points are nonuniformly expanding},
  author = {Xiongping Dai},
  journal= {arXiv preprint arXiv:1206.2113},
  year   = {2012}
}

Comments

24 pages; accepted by Math. Z

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