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A method for proving that monotone twist maps have no invariant circles

Published online by Cambridge University Press:  19 September 2008

Irwin Jungreis
Irwin Jungreis
Affiliation:
Department of Mathematics, Harvard University, Cambridge, MA 02138, USA
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Abstract

We present an existence theorem for certain kinds of orbits of a monotone twist map and use it to obtain a criterion for proving that there are no invariant circles with a certain range of rotation numbers. We have used this criterion to prove (computer assisted) that the standard map has no invariant circles for several parameter values including k = 0.9718.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 11 , Issue 1 , March 1991 , pp. 79 - 84
Copyright
Copyright © Cambridge University Press 1991

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References

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