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Combinatorics of torus diffeomorphisms

Published online by Cambridge University Press:  22 September 2003

JAROSLAW KWAPISZ
JAROSLAW KWAPISZ
Affiliation:
Department of Mathematical Sciences, Montana State University, Bozeman, MT 59717-2400, USA (e-mail: [email protected] web page: http://www.math.montana.edu/˜jarek/)
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Abstract

We construct dynamical partitions of the torus for a diffeomorphism that is isotopic to the identity. The existence and the combinatorics of the partitions is solely determined by the rotation set of the diffeomorphism. When the rotation set consists of a single non-resonant vector, there is a whole hierarchy of partitions analogous to the partitions of the circle into the closest return intervals under an irrational circle rotation. In particular, all such torus maps are infinitely renormalizable in a natural sense.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 23 , Issue 2 , April 2003 , pp. 559 - 586
Copyright
2003 Cambridge University Press

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