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Non-hyperbolic ergodic measures and horseshoes in partially hyperbolic homoclinic classes (1803.06572v2)
Published 17 Mar 2018 in math.DS
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.
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