Good Inducing Schemes for Uniformly Hyperbolic Flows, and Applications to Exponential Decay of Correlations

IF 1.4 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Annales Henri Poincaré Pub Date : 2024-04-25 DOI:10.1007/s00023-024-01439-w

Ian Melbourne, Paulo Varandas

引用次数: 0

Abstract

Given an Axiom A attractor for a \(C^{1+\alpha }\) flow (\(\alpha >0\)), we construct a countable Markov extension with exponential return times in such a way that the inducing set is a smoothly embedded unstable disk. This avoids technical issues concerning irregularity of boundaries of Markov partition elements and enables an elementary approach to certain questions involving exponential decay of correlations for SRB measures.

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均匀双曲流动的良好诱导方案及其在相关性指数衰减中的应用

给定一个（C^{1+\alpha }\ ）流（\(\alpha >0\)）的公理A吸引子，我们以诱导集是平滑嵌入的不稳定盘的方式构造一个具有指数返回时间的可数马尔可夫扩展。这避免了有关马尔可夫分区元素边界不规则性的技术问题，并使我们能够用一种基本方法来解决涉及 SRB 度量相关性指数衰减的某些问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annales Henri Poincaré 物理-物理：粒子与场物理

CiteScore

3.00

自引率

6.70%

发文量

108

审稿时长

6-12 weeks

期刊介绍： The two journals Annales de l''Institut Henri Poincaré, physique théorique and Helvetica Physical Acta merged into a single new journal under the name Annales Henri Poincaré - A Journal of Theoretical and Mathematical Physics edited jointly by the Institut Henri Poincaré and by the Swiss Physical Society. The goal of the journal is to serve the international scientific community in theoretical and mathematical physics by collecting and publishing original research papers meeting the highest professional standards in the field. The emphasis will be on analytical theoretical and mathematical physics in a broad sense.