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The fractal dimension of quasi-periodic orbits

Published online by Cambridge University Press:  01 December 1998

BRYAN P. RYNNE
BRYAN P. RYNNE
Affiliation:
Department of Mathematics, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, UK (e-mail: bryan@ma.hw.ac.uk)
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Abstract

Recently, Naito considered quasi-periodic orbits of Hölder continuous functions and obtained results relating the exponent in the Hölder condition to the asymptotic behaviour of the inclusion lengths of the $\epsilon$-almost periods of these orbits, and also to the fractal dimension of these orbits. In this paper we improve these results.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 18 , Issue 6 , December 1998 , pp. 1467 - 1471
Copyright
1998 Cambridge University Press

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