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Fractal dimensions of almost periodic attractors

Published online by Cambridge University Press:  19 September 2008

Koichiro Naito
Koichiro Naito
Affiliation:
Kumamoto University, Department of Mathematics, Faculty of Engineering, Kurokami 2-39-1, Kumamoto 860Japan (email: naito@sonata.tech.kumamoto-u.ac.jp or knaito@gpo.kumamoto-u.ac.jp)
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Abstract

In this paper we estimate fractal dimensions of almost periodic orbits in terms of two kinds of exponents: the exponent in the inclusion lengths for ε-almost period and the exponent in Hölder conditions. Further, we estimate the inclusion lengths for ε-almost period of quasi-periodic functions by using Diophantine approximations. In the n-frequency quasi-periodic case we can show that the fractal dimension of its orbit is majorized by the value n/δ when it is Hölder continuous with exponent δ, 0 < δ ≤ 1.

Type
Survey Article
Information
Ergodic Theory and Dynamical Systems , Volume 16 , Issue 4 , August 1996 , pp. 791 - 803
Copyright
Copyright © Cambridge University Press 1996

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References

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