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# Title: Non-hyperbolic ergodic measures and horseshoes in partially homoclinic classes

Abstract: We study a rich family of robustly non-hyperbolic transitive diffeomorphisms and we show that each ergodic measure is approached by hyperbolic sets in weak$*$-topology and in entropy. For hyperbolic ergodic measures, it is a classical result of A. Katok. The novelty here is to deal with non-hyperbolic ergodic measures.
 Comments: 25 pages and 1 figure Subjects: Dynamical Systems (math.DS) Cite as: arXiv:1803.06572 [math.DS] (or arXiv:1803.06572v1 [math.DS] for this version)

## Submission history

From: Jinhua Zhang [view email]
[v1] Sat, 17 Mar 2018 21:24:39 GMT (35kb)