Recurrent dimensions of quasi-periodic solutions for nonlinear evolution equations
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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.References
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Additional Information
- Koichiro Naito
- Affiliation: Faculty of Engineering, Kumamoto University, Kurokami 2-39-1, Kumamoto, 860-8555, Japan
- Email: naito@cs.kumamoto-u.ac.jp
- Received by editor(s): October 29, 2000
- Received by editor(s) in revised form: May 9, 2001
- Published electronically: September 21, 2001
- © Copyright 2001 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 354 (2002), 1137-1151
- MSC (2000): Primary 11K60, 28A80, 35B15
- DOI: https://doi.org/10.1090/S0002-9947-01-02901-4
- MathSciNet review: 1867375