On C¹-class local diffeomorphisms whose periodic points are nonuniformly expanding

2012/06/11 by Xiongping Dai, Dai, Xiongping
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.DS #msc:37D05 #msc:37D20 #msc:37D25

paper · pdf · doi:10.48550/arxiv.1206.2113

24 pages; accepted by Math. Z

arxiv created 2012/06/11 · arxiv updated 2012/06/12

Abstract

Using a sifting-shadowing combination, we prove in this paper that an arbitrary C¹-class local diffeomorphism f of a closed manifold Mⁿ is uniformly expanding on the closure Cl_Mⁿ(Per(f)) of its periodic point set Per(f), if it is nonuniformly expanding on Per(f).

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