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In this article, we consider the weighted ergodic optimization problem Axiom A attractors of a $C^2$ flow on a compact smooth manifold. The main result obtained in this paper is that for a generic observable from function space $mc C^{0,a}$ ($ain(0,1]$) or $mc C^1$ the minimizing measure is unique and is supported on a periodic orbit.
In this article, we consider the weighted ergodic optimization problem of a class of dynamical systems $T:Xto X$ where $X$ is a compact metric space and $T$ is Lipschitz continuous. We show that once $T:Xto X$ satisfies both the {em Anosov shadowing
For Axiom A flows on basic sets satisfying certain additional conditions we prove strong spectral estimates for Ruelle transfer operators similar to these of Dolgopyat (1998) for geodesic flows on compact surfaces (for general potentials)and transiti
We survey the impact of the Poincare recurrence principle in ergodic theory, especially as pertains to the field of ergodic Ramsey theory.
This survey is an update of the 2008 version, with recent developments and new references.
Let ${T^t}$ be a smooth flow with positive speed and positive topological entropy on a compact smooth three dimensional manifold, and let $mu$ be an ergodic measure of maximal entropy. We show that either ${T^t}$ is Bernoulli, or ${T^t}$ is isomorphi