Some remarks on Birkhoff and Mather twist map theorems
- 1 June 1982
- journal article
- research article
- Published by Cambridge University Press (CUP) in Ergodic Theory and Dynamical Systems
- Vol. 2 (2) , 185-194
- https://doi.org/10.1017/s0143385700001504
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.Keywords
This publication has 3 references indexed in Scilit:
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- On the ergodic properties of nowhere dispersing billiardsCommunications in Mathematical Physics, 1979
- CHARACTERISTIC LYAPUNOV EXPONENTS AND SMOOTH ERGODIC THEORYRussian Mathematical Surveys, 1977