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Recurrent dimensions of quasi-periodic solutions for nonlinear evolution equations


Author: Koichiro Naito
Journal: Trans. Amer. Math. Soc. 354 (2002), 1137-1151
MSC (2000): Primary 11K60, 28A80, 35B15
Published electronically: September 21, 2001
MathSciNet review: 1867375
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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.


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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

DOI: https://doi.org/10.1090/S0002-9947-01-02901-4
Keywords: Diophantine approximation, quasi-periodic solutions, fractal dimension
Received by editor(s): October 29, 2000
Received by editor(s) in revised form: May 9, 2001
Published electronically: September 21, 2001
Article copyright: © Copyright 2001 American Mathematical Society