标题： 基于伪谱方法的转移算子Ruelle共振的严格数值估计 显示英文标题

标题： A pseudospectral approach to rigorous numerical estimation of Ruelle resonances of transfer operators

摘要： 共振是作用在适当选择的巴拿赫空间上的转移算子的孤立特征值，在理解混沌动力系统统计性质中起着基础性作用。 在本文中，我们引入了一种伪谱方法，受Householder定理的启发，用于严格、计算机辅助的共振估计，提供了共振必须存在的区域，并排除了其他地方存在共振的可能性。 该方法具有普遍性，适用于各种混沌系统的转移算子，包括Anosov/Axiom A微分同胚和分段扩张映射。 我们对该方法进行了计算实现，针对圆周上的解析均匀扩张映射类。 我们预计，这里开发的伪谱框架将广泛适用于动力系统及其他领域的谱问题。 显示英文摘要

摘要： Resonances, isolated eigenvalues of a transfer operator acting on suitably chosen Banach spaces, play a fundamental role in understanding the statistical properties of chaotic dynamical systems. In this paper, we introduce a pseudospectral approach, inspired by Householder's theorem, for the rigorous, computer-assisted estimation of resonances, providing regions where resonances must exist and precluding the presence of resonances elsewhere. The approach is general, and applies to the transfer operators of a wide variety of chaotic systems, including Anosov/ Axiom A diffeomorphisms and piecewise expanding maps. We implement this approach computationally for a class of analytic uniformly expanding maps of the circle. We anticipate that the pseudospectral framework developed here will be broadly applicable to other spectral problems in dynamical systems and beyond.