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<p>We study equilibrium states for an open class of non-uniformly expanding local homeomorphisms defined by a mild condition requiring that for some iterate each point admits at least one contracting inverse branch. We prove the existence and uniqueness of equilibrium states and the differentiability of statistical quantities (such as the equilibrium states and the free energy function) with respect to the dynamical system.</p>

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Regularity, Linear Response Formula and Differentiability of the Free Energy for Non-uniformly Expanding Local Homeomorphisms

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月7日

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  • Carlos Bocker,
  • Ricardo Bortolotti,
  • Armando Castro,
  • Sávio Santana

摘要

We study equilibrium states for an open class of non-uniformly expanding local homeomorphisms defined by a mild condition requiring that for some iterate each point admits at least one contracting inverse branch. We prove the existence and uniqueness of equilibrium states and the differentiability of statistical quantities (such as the equilibrium states and the free energy function) with respect to the dynamical system.