Path connectedness and entropy density of the space of ergodic hyperbolic measures
arXiv:1505.02216
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.
9 pages