Abstract We propose a general framework for proving that a compact, infinite-dimensional map has an invariant set on which the dynamics is semiconjugated to a subshift of finite type. The method is then applied to certain Poincare map of the Kuramoto-Sivashinsky PDE on the line with odd and periodic boundary conditions and with parameter ν = 0.1212 . We give a computer-assisted proof of the existence of symbolic dynamics and countable infinity of periodic orbits with arbitrary large periods.

中文翻译：

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无限维混沌的几何方法：线上 Kuramoto-Sivashinsky PDE 的符号动力学

摘要 我们提出了一个通用框架，用于证明紧凑的无限维映射具有不变集，在该集上，动力学半共轭到有限类型的子位移。然后将该方法应用于 Kuramoto-Sivashinsky PDE 在奇数和周期性边界条件和参数 ν = 0.1212 的线上的某些 Poincare 映射。我们给出了一个计算机辅助证明，证明符号动力学和具有任意大周期的周期性轨道的可数无穷大的存在。