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Some remarks on Birkhoff and Mather twist map theorems

Published online by Cambridge University Press:  19 September 2008

A. Katok
A. Katok
Affiliation:
Department of Mathematics, University of Maryland, College Park, Maryland 20742, USA
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Abstract

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A recent result of J. Mather [1] about the existence of quasi-periodic orbits for twist maps is derived from an appropriately modified version of G. D. Birkhoff's classical theorem concerning periodic orbits. A proof of Birkhoff's theorem is given using a simplified geometric version of Mather's arguments. Additional properties of Mather's invariant sets are discussed.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 2 , Issue 2 , June 1982 , pp. 185 - 194
Copyright
Copyright © Cambridge University Press 1982

References

REFERENCES

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[6]Katok, A. & Spatzier, R.. Problem list of special session on differential geometry and ergodic theory in Amherst, October 1981. (Preprint.)Google Scholar