\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

Every ergodic measure is uniquely maximizing

Abstract Related Papers Cited by
  • Let $M_{\phi}$ denote the set of Borel probability measures invariant under a topological action $\phi$ on a compact metrizable space $X$. For a continuous function $f:X\to\R$, a measure $\mu\in\M_{\phi}$ is called $f$-maximizing if $\int f\, d\mu = s u p\{\int f dm:m\in\M_{\phi}\}$. It is shown that if $\mu$ is any ergodic measure in $\M_{\phi}$, then there exists a continuous function whose unique maximizing measure is $\mu$. More generally, if $\mathcal E$ is a non-empty collection of ergodic measures which is weak$^*$ closed as a subset of $\M_{\phi}$, then there exists a continuous function whose set of maximizing measures is precisely the closed convex hull of $\mathcal E$. If moreover $\phi$ has the property that its entropy map is upper semi-continuous, then there exists a continuous function whose set of equilibrium states is precisely the closed convex hull of $\mathcal E$.
    Mathematics Subject Classification: Primary: 37D35; Secondary: 37A05, 37A60, 37B99, 37D20, 54H15.

    Citation:

    \begin{equation} \\ \end{equation}
  • 加载中
SHARE

Article Metrics

HTML views() PDF downloads(115) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return