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Propriétés des attracteurs de Birkhoff

Published online by Cambridge University Press:  19 September 2008

P. Le Calvez
P. Le Calvez
Affiliation:
Université Paris-Sud et UA1169 du CNRS Mathématiques, Batiment 425, F-91405 Orsay cedex, France
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Abstract

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We study dissipative twist maps of the annulus, following the ideas of G. D. Birkhoff explained in an article of 1932.

In the first part, we give complete and rigorous proofs of the results of this article. We define the Birkhoff attractor of a dissipative twist map which has an attracting bounded annulus, we give its main properties and we define its upper and lower rotation numbers.

In the second part we give further results on these sets, thus we show that they often coincide with the closure of a hyperbolic periodic point and that they can contain an infinite number of sinks. We also show that the Birkhoff attractors don't depend on a continuous way on the maps.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 8 , Issue 2 , June 1988 , pp. 241 - 310
Copyright
Copyright © Cambridge University Press 1988

References

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