AC 1 make or break lemma |
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| Authors: | Shuhei Hayashi |
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| Affiliation: | (1) Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, 153-8914 Meguro, Tokyo, Japan |
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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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| Keywords: | homoclinic orbits connecting lemma Morse-Smale systems Kupka-Smale systems ergodic measures generic properties |
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