General Expansiveness for Diffeomorphisms from the Robust and Generic Properties
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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.
KeywordsExpansive n-expansive Quasi-Anosov Ω-stable
Mathematics Subject Classification (2010)37C20 37D20
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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