Recurrent dimensions of quasi-periodic solutions for nonlinear evolution equations

Naito, Koichiro

doi:10.1090/S0002-9947-01-02901-4

Recurrent dimensions of quasi-periodic solutions for nonlinear evolution equations
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Trans. Amer. Math. Soc. 354 (2002), 1137-1151 Request permission

Abstract:

In this paper we introduce recurrent dimensions of discrete dynamical systems and we give upper and lower bounds of the recurrent dimensions of the quasi-periodic orbits. We show that these bounds have different values according to the algebraic properties of the frequency and we investigate these dimensions of quasi-periodic trajectories given by solutions of a nonlinear PDE.

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