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Far East Journal of Dynamical Systems

Far East Journal of Dynamical Systems
Volume 2, Issue 1, Pages 53 - 69 (December 2000)

POINCARÉ RECURRENCES FOR RHYTHMICAL DYNAMICS
V. Afraimovich, E. Ugalde (Mexico) and J. Urías (USA)

Abstract:
We introduce and study systems with discrete time such that temporal intervals between two successive iterations of a map depend on a point and the number of the iteration, i.e., we deal with rhythmical dynamics. We derive formulas for spectra of dimensions for Poincaré recurrences in two extreme cases. In the first case the temporal interval between two successive iterations depends only on the position of the point; in the second one it depends only on the integer time. These formulae are of the Bowen type nonhomogeneous equations.

Keywords and phrases: dimension theory, Poincaré recurrences, rhythmical dynamics.

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P-ISSN: 0972-1118

E-ISSN: 3048-7897

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