A symplectic proof of a theorem of Franks
Symplectic Geometry
2019-02-20 v2 Dynamical Systems
Abstract
A celebrated theorem in two-dimensional dynamics due to John Franks asserts that every area preserving homeomorphism of the sphere has either two or infinitely many periodic points. In this work we reprove Franks' theorem under the additional assumption that the map is smooth. Our proof uses only tools from symplectic topology and thus differs significantly from all previous proofs. A crucial role is played by the results of Ginzburg and Kerman concerning resonance relations for Hamiltonian diffeomorpisms.
Keywords
Cite
@article{arxiv.1107.1282,
title = {A symplectic proof of a theorem of Franks},
author = {Brian Collier and Ely Kerman and Benjamin M. Reiniger and Bolor Turmunkh and Andrew Zimmer},
journal= {arXiv preprint arXiv:1107.1282},
year = {2019}
}
Comments
15 pages. Minor changes. Final version to appear in Compositio Mathematica