A Topological Version of a Theorem of Mather on Twist Maps.
Technical summary rept.,
WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
Pagination or Media Count:
In this report shows that a twist map of an annulus with a periodic point of rotation number pq must have a Birkhoff periodic point of rotation number pq. Topological techniques are used so no assumption of area-preservation or circle intersection property is needed. If the map is area preserving then this theorem and the fixed point theorem of Birkhoff imply a recent theorem of Mather. It is also shown that periodic orbits of significantly smallest period for a twist map must be Birkhoff. Author
- Celestial Mechanics
- Theoretical Mathematics