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STOCHASTIC POTENTIALS OF INTERMITTENT MAPS
Published online by Cambridge University Press: 18 June 2020
Abstract
Consider an intermittent map $f_{\unicode[STIX]{x1D705}}:[0,1]\rightarrow [0,1]$ and a Hölder continuous potential
$\unicode[STIX]{x1D711}:[0,1]\rightarrow \mathbb{R}$. We show that
$\unicode[STIX]{x1D719}$ is stochastic for
$f_{\unicode[STIX]{x1D705}}$ if and only if the topological pressure
$P(f_{\unicode[STIX]{x1D705}},\unicode[STIX]{x1D711})$ satisfies
$P(f_{\unicode[STIX]{x1D705}},\unicode[STIX]{x1D711})-\unicode[STIX]{x1D711}(0)>0$. As a consequence, for each
$\unicode[STIX]{x1D6FD}>0$ sufficiently small, the set of Hölder continuous potentials of exponent
$\unicode[STIX]{x1D6FD}$ that are not stochastic for
$f_{\unicode[STIX]{x1D705}}$ has nonempty interior in the space of all such potentials.
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 103 , Issue 1 , February 2021 , pp. 145 - 153
- Copyright
- © 2020 Australian Mathematical Publishing Association Inc.
Footnotes
The author was supported by the National Natural Science Foundation of China (Grant No. 11871194).