Maximizing measures in hyperbolic dynamics

双曲动力学测度最大化

• 批准号: EP/E020801/1
• 负责人: Mark Pollicott
• 金额: $ 32.06万
• 依托单位: University of Warwick
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2007
• 资助国家: 英国
• 起止时间: 2007 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FE020801%2F1
• 关键词: Maximizing; measures; hyperbolic; dynamics

In the study of dynamical systems, the long term asymptotic behaviour is often best understood in terms of properties of invariant measures. In the particular setting of Lagrangian flows, Mane and Mather formulated a number of important questions about those measures whose integrals maximized a particular integral. As part of a general theory, one can ask similar questions about quite diverse dynamical systems. In the particular case of hyperbolic (or chaotic) dynamical systems, we can consider a natural class of measures called Gibbs measures, whose study originated in the mathematical theory of Statistical Mechanics, and the work of Ruelle and Sinai. This proposal relates to how maximizing measures for typical functions for these hyperbolic systems can be approximated by these better behaved Gibbs measures. This has important implications for understanding the quite complicated, but important, maximizing measures in terms of much simpler Gibbs measures.

在动态系统的研究中，通常最好从不变措施的性质来理解长期的渐近行为。在拉格朗日流的特定环境中，Mane和Mather提出了许多重要的问题，这些措施的积分最大化了特定的积分。作为一般理论的一部分，人们可以就多样化的动态系统提出类似的问题。在双曲线（或混乱）动力学系统的特殊情况下，我们可以考虑一种自然的措施，称为Gibbs度量，其研究起源于统计力学的数学理论以及Ruelle和Sinai的工作。该建议与这些表现更好的吉布斯度量近似近似这些双曲线系统的典型功能的措施如何最大程度地涉及。这对于理解相当复杂但重要的，从更简单的吉布斯度量方面最大化措施具有重要意义。

项目成果

How Many Inflections are There in the Lyapunov Spectrum?

• DOI: 10.1007/s00220-021-04161-4
• 发表时间: 2020-02
• 期刊: Communications in Mathematical Physics
• 影响因子: 2.4
• 作者: O. Jenkinson;M. Pollicott;P. Vytnova

Thermodynamic Formalism - CIRM Jean-Morlet Chair, Fall 2019

热力学形式主义 - CIRM Jean-Morlet 主席，2019 年秋季

• DOI: 10.1007/978-3-030-74863-0_12
• 发表时间: 2021
• 作者: Pollicott M

Two bifurcation sets arising from the beta transformation with a hole at 0

由 0 处有孔的 beta 变换产生的两个分叉集

• DOI: 10.1016/j.indag.2020.03.001
• 发表时间: 2020
• 期刊: Indagationes Mathematicae
• 作者: Baker S

Uniform lower bounds on the dimension of Bernoulli convolutions

伯努利卷积维数的统一下界

• DOI: 10.1016/j.aim.2021.108090
• 发表时间: 2022
• 期刊: Advances in Mathematics
• 影响因子: 1.7
• 作者: Kleptsyn V

Exceptional digit frequencies and expansions in non-integer bases

特殊的数字频率和非整数基数的扩展

• DOI: 10.1007/s00605-019-01311-8
• 发表时间: 2019
• 期刊: Monatshefte für Mathematik
• 作者: Baker S