Abstract
In the stochastic context, an invariant set is decomposed into the union of ergodic basins, and each of basin possesses the fractal structure determined by ergodic measures. This paper is to show that when a hyperbolic SRB measure is mixing, the set of measures with zero entropy and the set of measures with positive entropy but without SRB are both dense on the set of all invariant measures on the closure of the ergodic basin in the Pesin set, and moreover that in the set of invariant measures as above a measure with ergodicity and SRB exists uniquely.
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