A geometric method for infinite-dimensional chaos: Symbolic dynamics for the Kuramoto-Sivashinsky PDE on the line

[摘要] 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 nu = 0.1212. We give a computer-assisted proof of the existence of symbolic dynamics and countable infinity of periodic orbits with arbitrary large periods. (c) 2020 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

[发布日期] 2020-11-05

[关键词] Symbolic dynamics;Periodic orbits;Dissipative PDEs;Galerkin projection;Rigorous numerics;Computer-assisted proof