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A dichotomy for a two-parameter piecewise rotation

Published online by Cambridge University Press:  20 June 2003

MICHAEL BOSHERNITZAN  and
AREK GOETZ
MICHAEL BOSHERNITZAN
Affiliation:
Department of Mathematics, Rice University, 6100 S. Main St., Houston, TX 77005-1892, USA (e-mail: [email protected])
AREK GOETZ
Affiliation:
Department of Mathematics, San Francisco State University, 1600 Holloway Avenue, San Francisco, CA 94132, USA (e-mail: [email protected])
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Abstract

We investigate a basic system T of two rotations with a common angle of rotation. Using a new idea, we prove that, except for an invertible T, the system T must have a global attractor and a global repeller. We give a specific condition for both cases.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 23 , Issue 3 , June 2003 , pp. 759 - 770
Copyright
2003 Cambridge University Press

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