Abstract
AbstractA 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.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,General Mathematics
Cited by
84 articles.
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1. Twist Maps of the Annulus: An Abstract Point of View;Regular and Chaotic Dynamics;2023-04-10
2. Global Dynamics of the Breathing Circle Billiard;Qualitative Theory of Dynamical Systems;2022-07-25
3. Chaotic Dynamics of Monotone Twist Maps;Acta Mathematica Sinica, English Series;2022-01
4. On the global dynamical properties of a Fermi–Ulam model;Journal of Difference Equations and Applications;2021-11-17
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