对双曲流遍历理论的贡献：准不变度量的唯一遍历性和时间一映射的均衡状态

IF 0.8 2区数学 Q2 MATHEMATICS

Israel Journal of Mathematics Pub Date : 2023-12-18 DOI:10.1007/s11856-023-2588-3

Pablo D. Carrasco, Federico Rodriguez-Hertz

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引用次数: 0

摘要

我们考虑了与阿诺索夫流或衍射（拓扑混合）相对应的角环流，并建立了具有赫尔德雅各比的横向准不变度量的唯一性。在同样的背景下，我们给出了双曲系统平衡态的精确特征，证明了在角环流叶面上存在一个 Radon 度量族，使得任何概率（不变或非不变），只要具有这个族给出的条件，就必然是系统的唯一平衡态。

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Contributions to the ergodic theory of hyperbolic flows: unique ergodicity for quasi-invariant measures and equilibrium states for the time-one map

We consider the horocyclic flow corresponding to a (topologically mixing) Anosov flow or diffeomorphism, and establish the uniqueness of transverse quasi-invariant measures with Hölder Jacobians. In the same setting, we give a precise characterization of the equilibrium states of the hyperbolic system, showing that existence of a family of Radon measures on the horocyclic foliation such that any probability (invariant or not) having conditionals given by this family, necessarily is the unique equilibrium state of the system.

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来源期刊

Israel Journal of Mathematics 数学-数学

CiteScore

1.70

自引率

10.00%

发文量

审稿时长

6 months

期刊介绍： The Israel Journal of Mathematics is an international journal publishing high-quality original research papers in a wide spectrum of pure and applied mathematics. The prestigious interdisciplinary editorial board reflects the diversity of subjects covered in this journal, including set theory, model theory, algebra, group theory, number theory, analysis, functional analysis, ergodic theory, algebraic topology, geometry, combinatorics, theoretical computer science, mathematical physics, and applied mathematics.