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A forward Ergodic Closing Lemma and the Entropy Conjecture for nonsingular endomorphisms away from tangencies
2020
Discrete and Continuous Dynamical Systems. Series A
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We prove a forward Ergodic Closing Lemma for nonsingular C 1 endomorphisms, claiming that the set of eventually strongly closable points is a total probability set. The "forward" means that the closing perturbation is involved along a finite part of the forward orbit of a point in a total probability set, which is the same perturbation as in Mañé's Ergodic Closing Lemma for C 1 diffeomorphisms. As an application, Shub's Entropy Conjecture for nonsingular C 1 endomorphisms away from homoclinic
doi:10.3934/dcds.2020114
fatcat:3zg45dmsubd2xlh2k4d7c2we7e