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A topological version of a theorem of Mather on twist maps

Published online by Cambridge University Press:  19 September 2008

Glen Richard Hall
Glen Richard Hall
Affiliation:
Department of Mathematics, Boston University, Boston, MA 02215, USA
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Abstract

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In this report we show that a twist map of an annulus with a periodic point of rotation number p/q must have a Birkhoff periodic point of rotation number p/q. We use topological techniques so no assumption of area-preservation or circle intersection property is needed. If the map is area-preserving then this theorem andthe fixed point theorem of Birkhoff imply a recent theorem of Aubry and Mather. We also show that periodic orbits of (significantly) smallest period for a twist map must be Birkhoff.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 4 , Issue 4 , December 1984 , pp. 585 - 603
Copyright
Copyright © Cambridge University Press 1984

References

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