丛状吸引子上平衡态的傅里叶衰减
动力系统
2023-01-26 v1
摘要
设 为闭流形， 为一个 的 Axiom A 微分同胚。假设 有一个余维为 1 的稳定层化吸引子 。在一般的非线性条件与适当的丛状条件下，我们证明了 上一大类不变测度在不稳定方向上的多项式傅里叶衰减。我们的结果特别适用于极大熵测度。我们在附录中构造了一个满足非线性与丛状假设的显式螺线管。
引用
@article{arxiv.2301.10623,
title = {Fourier decay of equilibrium states for bunched attractors},
author = {Gaétan Leclerc},
journal= {arXiv preprint arXiv:2301.10623},
year = {2023}
}
备注
This is a first work on trying to understand the Fourier transform of equilibrium states for Axiom A diffeomorphisms using Markov partitions. This is part of the author's PhD and might not be published soon, as we are working on another approach that might gives better results