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Coupling two unimodal maps with simple kneading sequences

Published online by Cambridge University Press:  02 February 2004

BASTIEN FERNANDEZ  and
MIAOHUA JIANG
BASTIEN FERNANDEZ
Affiliation:
Centre de Physique Théorique (FRUMAM), CNRS Luminy Case 907, 13288 Marseille CEDEX 09, France (e-mail: [email protected])
MIAOHUA JIANG
Affiliation:
Department of Mathematics, Wake Forest University, Winston Salem, NC 27109, USA (e-mail: [email protected])
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Abstract

The dynamics of a system of two diffusively coupled identical unimodal maps is investigated. The unimodal maps have simple kneading sequences which imply that their orbits are asymptotically periodic with period a power of two. Analogous results are obtained for the coupled system for all coupling parameters. We prove the eventual periodicity of the position of orbits with respect to the diagonal of the square phase space and the asymptotic periodicity for orbits whose coordinates have the same sign. Finally, we give a global condition for the existence of symmetric orbits that are examples of orbits with this asymptotic property.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 24 , Issue 1 , February 2004 , pp. 107 - 125
Copyright
2004 Cambridge University Press

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