AI 中文总结
本文针对具有多个中性不动点的间歇映射与不连续势函数发展热力学形式主义，证明满足双曲性假设时存在具正熵且关联指数衰减的唯一平衡态，还刻画了单参数族的相变并证明临界参数处多平衡态可共存，方法基于共形测度分析。
AI 中文摘要
本文针对具有有限个中性不动点的全分支区间间歇映射，以及一大类可能不连续的势函数，发展了热力学形式主义。在势函数满足双曲性假设下，我们证明存在唯一的平衡态，其具有正熵且关联呈指数衰减。此外，我们对单参数族βφ（β>0）刻画了其相变，并证明在临界参数处，多个遍历平衡态可能共存，其中至多一个具有正熵。我们的方法依赖于对共形测度的详细分析。
英文摘要
In this paper, we develop the thermodynamic formalism for intermittent full-branch interval maps with finitely many neutral fixed points and for a broad class of possibly discontinuous potentials. Under a hyperbolicity assumption on the potential, we prove the existence of a unique equilibrium state with positive entropy and exponential decay of correlations. Furthermore, we characterize the phase transitions for the one-parameter family $βφ$, with $β>0$, and prove that, at the critical parameter, multiple ergodic equilibrium states may coexist, at most one of which has positive entropy. Our approach relies on a detailed analysis of conformal measures.
Comments34 pages
