Some remarks on Birkhoff and Mather twist map theorems

A. Katok

doi:10.1017/S0143385700001504

Some remarks on Birkhoff and Mather twist map theorems

A. Katok

Research output: Contribution to journal › Article › peer-review

92 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	185-194
Number of pages	10
Journal	Ergodic Theory and Dynamical Systems
Volume	2
Issue number	2
DOIs	https://doi.org/10.1017/S0143385700001504
State	Published - Jun 1982

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

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title = "Some remarks on Birkhoff and Mather twist map theorems",

abstract = "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.",

author = "A. Katok",

year = "1982",

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AB - 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.

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JO - Ergodic Theory and Dynamical Systems

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ER -

Some remarks on Birkhoff and Mather twist map theorems

Abstract

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