通过诱导方案实现双曲势的平衡态 *

IF 1.6 2区 数学 Q2 MATHEMATICS, APPLIED Nonlinearity Pub Date : 2024-08-13 DOI:10.1088/1361-6544/ad6b6e
José F Alves, Krerley Oliveira, Eduardo Santana
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引用次数: 0

摘要

在非均匀扩展映射(可能存在临界集)的背景下,我们证明了双曲势存在有限多个遍历平衡态。此外,这些平衡态都是膨胀量。这概括了拉莫斯和维亚纳的一个结果,在这个结果中,分析方法被用于没有临界集的映射。这里的策略包括使用有限数量的具有马尔可夫结构的诱导方案,用无限多的符号对动力学进行编码,以获得相关符号动力学的平衡态,然后再对其进行投影,以获得原始映射的平衡态。我们将结果应用于多维维亚纳映射这一重要类别。
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Equilibrium states for hyperbolic potentials via inducing schemes *
In a context of non-uniformly expanding maps, possibly with the presence of a critical set, we prove the existence of finitely many ergodic equilibrium states for hyperbolic potentials. Moreover, the equilibrium states are expanding measures. This generalizes a result due to Ramos and Viana, where analytical methods are used for maps with no critical sets. The strategy here consists in using a finite number of inducing schemes with a Markov structure in infinitely many symbols to code the dynamics, to obtain an equilibrium state for the associated symbolic dynamics and then projecting it to obtain an equilibrium state for the original map. We apply our results to the important class of multidimensional Viana maps.
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来源期刊
Nonlinearity
Nonlinearity 物理-物理:数学物理
CiteScore
3.00
自引率
5.90%
发文量
170
审稿时长
12 months
期刊介绍: Aimed primarily at mathematicians and physicists interested in research on nonlinear phenomena, the journal''s coverage ranges from proofs of important theorems to papers presenting ideas, conjectures and numerical or physical experiments of significant physical and mathematical interest. Subject coverage: The journal publishes papers on nonlinear mathematics, mathematical physics, experimental physics, theoretical physics and other areas in the sciences where nonlinear phenomena are of fundamental importance. A more detailed indication is given by the subject interests of the Editorial Board members, which are listed in every issue of the journal. Due to the broad scope of Nonlinearity, and in order to make all papers published in the journal accessible to its wide readership, authors are required to provide sufficient introductory material in their paper. This material should contain enough detail and background information to place their research into context and to make it understandable to scientists working on nonlinear phenomena. Nonlinearity is a journal of the Institute of Physics and the London Mathematical Society.
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