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.

中文翻译：

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间歇性地图的随机潜力

考虑一个间歇性地图$f_{\unicode[STIX]{x1D705}}:[0,1]\rightarrow [0,1]$和 Hölder 连续势$\unicode[STIX]{x1D711}:[0,1]\rightarrow \mathbb{R}$. 我们表明$\unicode[STIX]{x1D719}$是随机的$f_{\unicode[STIX]{x1D705}}$当且仅当拓扑压力$P(f_{\unicode[STIX]{x1D705}},\unicode[STIX]{x1D711})$满足$P(f_{\unicode[STIX]{x1D705}},\unicode[STIX]{x1D711})-\unicode[STIX]{x1D711}(0)>0$. 因此，对于每个$\unicode[STIX]{x1D6FD}>0$足够小，指数的 Hölder 连续势集$\unicode[STIX]{x1D6FD}$不是随机的$f_{\unicode[STIX]{x1D705}}$在所有此类势的空间中具有非空内部。