成串吸引子平衡态的傅立叶衰减

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED Nonlinearity Pub Date : 2024-08-01 DOI:10.1088/1361-6544/ad6052

Gaétan Leclerc

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引用次数: 0

摘要

设 M 是封闭流形，设 f 是公理 A 差分变形。假设 f 有一个具有标度为 1 的稳定层理的吸引子 Ω。在一般非线性条件和合适的束化条件下，我们证明了Ω上一大类不变度量在不稳定方向上的多项式傅里叶衰减。我们的结果尤其适用于最大熵的度量。我们在附录中构建了一个满足非线性和束状假设的显式螺线管。

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Fourier decay of equilibrium states for bunched attractors

Let M be a closed manifold, and let be a Axiom A diffeomorphism. Suppose that f has an attractor Ω with codimension 1 stable lamination. Under a generic nonlinearity condition and a suitable bunching condition, we prove polynomial Fourier decay in the unstable direction for a large class of invariant measures on Ω. Our result applies in particular for the measure of maximal entropy. We construct in the appendix an explicit solenoid that satisfies the nonlinearity and bunching assumption.

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来源期刊

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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