论文标题
用于扩大措施的热力学形式主义
Thermodynamic formalism for expanding measures
论文作者
论文摘要
在本文中，我们研究了强烈的内态性质内态性$ F $的热力学形式主义，重点是所有扩展措施。如果$ f $是在riemannian歧管上定义的非flat $ c^{1+} $映射，则这些是不变的概率度量，其所有Lyapunov指数为正。考虑到Hölder连续潜在的$φ$，我们证明了扩展度量的空间之间平衡状态的独特性。此外，我们表明，扩展度量的存在$μ$最大化扩展措施空间的熵意味着平衡状态的存在和独特性$μ_φ$在扩大任何Hölder连续$ usportul unity $ uscill的措施的空间上，具有小振荡$ \ \ \ cosc {OSC {OSC} {OSC} {OSC} {OSC} {OSC} = c = \ sup feff feff feff feff feff或sup sup fiff feff feff \ sup。作为某些应用，我们证明Collet-Eckmann二次图不接受Hölder潜力的相变，并表明对于Viana地图和每个Hölder的每个Hölder的连续潜力都足够小，具有独特的平衡状态。
In this paper we study the thermodynamic formalism of strongly transitive endomorphisms $f$, focusing on the set all expanding measures. In case $f$ is a non-flat $C^{1+}$ map defined on a Riemannian manifold, these are invariant probability measures with all its Lyapunov exponents positive. Given a Hölder continuous potential $φ$ we prove the uniqueness of the equilibrium state among the space of expanding measures. Moreover, we show that the existence of an expanding measure $μ$ maximizing the entropy on the the space of expanding measures implies the existence and uniqueness of equilibrium state $μ_φ$ on the space of expanding measures for any Hölder continuous potential $φ$ with a small oscillation $\text{osc }φ=\supφ-\infφ$. As some applications, we prove that Collet-Eckmann quadratic maps does not admit phase transition for Hölder potential, and show that for Viana maps and every Hölder continuous potential of sufficiently small oscillation has a unique equilibrium state.
