A topological version of a theorem of Mather on twist maps
- 1 December 1984
- journal article
- research article
- Published by Cambridge University Press (CUP) in Ergodic Theory and Dynamical Systems
- Vol. 4 (4), 585-603
- https://doi.org/10.1017/s0143385700002662
Abstract
In this report we show that a twist map of an annulus with a periodic point of rotation number p/q must have a Birkhoff periodic point of rotation number p/q. We use topological techniques so no assumption of area-preservation or circle intersection property is needed. If the map is area-preserving then this theorem andthe fixed point theorem of Birkhoff imply a recent theorem of Aubry and Mather. We also show that periodic orbits of (significantly) smallest period for a twist map must be Birkhoff.Keywords
This publication has 1 reference indexed in Scilit:
- An Improvement of the Poincare-Birkhoff Fixed Point TheoremTransactions of the American Mathematical Society, 1982