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Path connectedness and entropy density of the space of ergodic hyperbolic measures

Published 9 May 2015 in math.DS | (1505.02216v2)

Abstract: We show that the space of hyperbolic ergodic measures of a given index supported on an isolated homoclinic class is path connected and entropy dense provided that any two hyperbolic periodic points in this class are homoclinically related. As a corollary we obtain that the closure of this space is also path connected.

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