Approximation property on entropies for surface diffeomorphisms

2018/03/19 by Wanlou Wu, Wu, Wanlou, Jiansong Liu +1 · 1 citation
Mathematics · Biochemistry, Genetics and Molecular Biology · #Mathematical Dynamics and Fractals #Caveolin-1 and cellular processes

paper · pdf · doi:10.48550/arxiv.1803.06863

Abstract

In this paper, we prove that for any C¹ surface diffeomorphism f with positive topological entropy, there exists a diffeomorphism g arbitrarily close (in the C¹ topology) to f exhibiting a horseshoe Λ, such that the topological entropy of g restricted on Λ can arbitrarily approximate the topological entropy of f. This extends the Theorem \cite[Theorem 1.1]Gan of Gan.

Cited by

• Entropy Flexibility of Dynamical Systems

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