Birkhoff Orbits for Non-Monotone Twist Maps.
Abstract
Recently it has been shown that twist maps of the annulus, which arise naturally in such diverse problems as the 3-body problem, billiards in a convex table and Hopf bifurcation of maps of the plane, possess many simple periodic orbits and quasi-periodic orbits. The original proofs of this used a variational technique requiring a globally defined action and which limited the theorem to so called monotone twist maps. The restriction to monotone twist maps is fairly severe since, for example, the composition of a monotone twist map with itself need not be a monotone twist map. Topological techniques may also be used to obtain these theorems and it is the purpose of this report to point out that, after suitably altering the definitions, the topological arguments apply to a much larger family of twist maps.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1984
- Accession Number
- ADA144718
Entities
People
- G. R. Hall
Organizations
- University of Wisconsin–Madison