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AC 1 make or break lemma

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Abstract

Mañé suggested the following question: Consider aC r flow on a compact manifold without boundary and suppose that the ω-limit set of a pointp intersets the α-limit set ofq, i.e. ω(p)∩α(q)≠Ø. Can the flow beC r-perturbed so that either (a)p is connected toq (p andq in the same orbit) or (b) ω(p)∩α(q)=Ø for the new flow? Here we solve positively a stronger version of this problem forC 1 small perturbations of the original flow.

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Authors and Affiliations

  1. Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, 153-8914, Meguro, Tokyo, Japan

    Shuhei Hayashi

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  1. Shuhei Hayashi
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Hayashi, S. AC 1 make or break lemma. Bol. Soc. Bras. Mat 31, 337–350 (2000). https://doi.org/10.1007/BF01241633

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  • DOI: https://doi.org/10.1007/BF01241633

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