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Rotation sets and Morse decompositions in twist maps

Published online by Cambridge University Press:  10 December 2009

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Abstract

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Positive tilt maps of the annulus are studied, and a correspondence is developed between the rotation set of the map and certain of its Morse decompositions. The main tool used is a characterization of fixed point free lifts of positive tilt maps. As an application, some alternative hypotheses under which the conclusions of the Aubry-Mather theorem hold are given, and it is also shown that the rotation band of a chain transitive set is always in the rotation set of the map.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 8 , Volume 8: Charles Conley Memorial Issue , December 1988 , pp. 33 - 61
Copyright
Copyright © Cambridge University Press 1988

References

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