A dichotomy for measures of maximal entropy near time-one maps of transitive Anosov flows (original) (raw)
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ENTROPY AND MEASURE DEGENERACY FOR FLOWS
2008
In discrete dynamical systems topological entropy is a topological invariant and a measurement of the complexity of a system. In continuous dynamical systems, in general, topological entropy defined as usual by the time one map does not work so well in what concerns these aspects. The point is that the natural notion of equivalence in the discrete case is topological conjugacy which preserves time while in the continuous case the natural notion of equivalence is topological equivalence which allow reparametrizations of the orbits. The main issue happens in the case that the system has fixed points and will be our subject here.
Boletim Da Sociedade Brasileira De Matematica, 1999
We introduce a concept of measure-theoretic entropy for flows and study its invariance under measure-theoretic equivalences. Invariance properties of the corresponding topological entropy is studied too. We also answer a question posed by Bowen-Walters in [3] concerning the equality between the topological entropy of the time-one map of an expansive flow and the time-one map of its symbolic suspension.