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General Expansiveness for Diffeomorphisms from the Robust and Generic Properties

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Abstract

Let f:M → M be a diffeomorphism on a closed smooth d(d ≥ 2)-dimensional manifold. For each \(n\in \mathbb N\), if f belongs to C 1-interior of the set of the n-expansive diffeomorphisms, then f satisfies quasi-Anosov. For C 1-generic f, if f is n-expansive then f satisfies both Axiom A and the no-cycle condition.

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Acknowledgments

The author wishes to express his deepest appreciation to the referee for his careful reading of the manuscript. This work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (No-2014R1A1A1A05002124).

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  1. Department of Mathematics, Mokwon University, Daejeon, 302-729, Korea

    Manseob Lee

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  1. Manseob Lee
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Correspondence to Manseob Lee.

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Lee, M. General Expansiveness for Diffeomorphisms from the Robust and Generic Properties. J Dyn Control Syst 22, 459–464 (2016). https://doi.org/10.1007/s10883-015-9288-1

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  • DOI: https://doi.org/10.1007/s10883-015-9288-1

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