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

Xiongping Dai

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arXiv · 1206.2113

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

Xiongping Dai

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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 $\mathrm{Per}(f)$.

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Xiongping Dai. 2012-06-11. On $\mathrm{C}^1$-class local diffeomorphisms whose periodic points are nonuniformly expanding. https://arxiv.org/abs/1206.2113

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