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Hyperbolic sets for twist maps

Published online by Cambridge University Press:  19 September 2008

Daniel L. Goroff
Daniel L. Goroff
Affiliation:
Department of Mathematics, Harvard University, Cambridge, MA 02138, USA
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Abstract

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An example is given of an area-preserving monotone twist map such that a uniformly hyperbolic structure exists on the closure of its Birkhoff maximizing orbits.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 5 , Issue 3 , September 1985 , pp. 337 - 339
Copyright
Copyright © Cambridge University Press 1985

References

REFERENCES

[1]André, G. & Aubry, S.. Annals of the Israel Physical Society 3 (1979), 133–164.Google Scholar
[2]Aubry, S.. The twist Map, the extended Frenkel-Kontorova model and the Devil's staircase. Physica D. 7 (1983), 240–258.CrossRefGoogle Scholar
[3]Aubry, S., Daeron, P. Y. Le & Andre, G., Classical ground-states of a one-dimensional model for incommensurate structures. Submitted for publication to Communications in Mathematical Physics.Google Scholar
[4]Katok, A.. Problem list of special session on differential geometry and ergodic theory in Amherst. Preprint1981.Google Scholar
[5]Katok, A.. Some remarks on Birkhoff and Mather twist map theorems. Ergod. Th. & Dynam. Syst. 2 (1982), 185–194.CrossRefGoogle Scholar
[6]Mather, J. N.. Existence of quasi-periodic orbits for twist homeomorphisms of the annulus. Topology 21 (1982), 457–467.CrossRefGoogle Scholar
[7]Mather, J. N.. Non-existence of invariant circles. Ergod. Th. & Dynam. Sys. To appear.Google Scholar
[8]Mather, J. N.. A criterion for the non-existence of invariant circles. Preprint, 1982.Google Scholar
[9]Newhouse, S. E.. Lectures on Dynamical Systems. In Guckenheimer, J., Moser, J. & Newhouse, S. E.. Dynamical Systems: C.I.M.E. Lectures. Birkhauser, 1980, pp. 1–114.Google Scholar
[10]Newhouse, S. E. & Palis, J.. Bifurcations of Morse-Smale dynamical systems. In Dynamical Systems (Peixoto, M., ed.). Academic Press, 1973, pp. 303–366.Google Scholar