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A sufficient condition for zero entropy

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Abstract

We prove that a diffeomorphism \(f\) defined on a compact manifold has zero topological entropy if there are \(d\in {\mathbb {N}}\) and \(K>0\) such that \(\Vert Dg^{n_x}(x)\Vert \le Kn^d_x\) for every diffeomorphism \(g\) that is \(C^1\) close to \(f\) and every periodic point \(x\) of least period \(n_x\) of \(g\).

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Authors and Affiliations

  1. Instituto de Matemática, Universidade Federal do Rio de Janeiro, P. O. Box 68530, Rio de Janeiro, 21945-970, Brazil

    A. Arbieto & C. Morales

Authors
  1. A. Arbieto
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  2. C. Morales
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Corresponding author

Correspondence to C. Morales.

Additional information

Communicated by H. Bruin.

Partially supported by CNPq, FAPERJ and PRONEX/DYN-SYS. from Brazil.

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Arbieto, A., Morales, C. A sufficient condition for zero entropy. Monatsh Math 175, 323–332 (2014). https://doi.org/10.1007/s00605-014-0608-4

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  • DOI: https://doi.org/10.1007/s00605-014-0608-4

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