发表机构
Pontificia Universidad Católica de Valparaíso; Pontificia Universidad Católica de Chile; Universidad Católica del Norte（智利天主教瓦帕拉索大学; 智利天主教大学; 智利北部天主教大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究d维环面上与线性Anosov自同构同痕的部分双曲微分同胚的拓扑熵，证明一类DA映射的拓扑熵与线性映射一致，得到低振荡势的平衡态唯一性等结果，还构造出拓扑熵严格大于线性部分的动态相容微分同胚。
AI 中文摘要
本文研究了d维环面$\boldsymbol{\top}^d$上、与线性Anosov自同构同痕且具有不可分解弱稳定子空间的部分双曲微分同胚的拓扑熵行为。特别地，我们证明对于这类线性系统对应的一类DA映射，当其中心行为被线性模型的膨胀率充分控制时，其拓扑熵与线性映射的拓扑熵一致。此外，我们得到了一类低振荡势的平衡态唯一性，并作为应用得到了最大熵测度的唯一性。我们还给出了遍历测度成为某连续势的唯一平衡态的充分条件。最后，在$\boldsymbol{\top}^3$上，我们构造了同一同痕类中一个动态相容的微分同胚，其拓扑熵严格大于线性部分的拓扑熵。
英文摘要
In this paper we study the behavior of topological entropy for partially hyperbolic diffeomorphisms on $\mathbb{T}^d$ isotopic to a linear Anosov automorphism with indecomposable weak-stable subspace. In particular, we prove that for a class of DA maps associated with such linear systems, whose central behavior is sufficiently dominated by the expansion rate of the linear model, the topological entropy coincides with that of the linear map. Furthermore, we obtain uniqueness of equilibrium states for a class of low-oscillation potentials and, as an application, the uniqueness of the measure of maximal entropy. We also provide sufficient conditions for which ergodic measures arise as the unique equilibrium state of some continuous potential. Finally, on $\mathbb{T}^3$ we construct a dynamically coherent diffeomorphism in the same isotopy class whose topological entropy is strictly larger than that of the linear part.
Comments33 pages, 2 Figures. Comments are welcome
