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 Poincaré 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.
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Wilczak et al. (2020) studied this question.
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