On the Hofer-Zehnder conjecture
Symplectic Geometry
2019-11-22 v2 Dynamical Systems
Abstract
We prove that if a Hamiltonian diffeomorphism of a closed monotone symplectic manifold with semisimple quantum homology has more contractible fixed points, counted homologically, than the total dimension of the homology of the manifold, then it must have an infinite number of contractible periodic points. This constitutes a higher-dimensional homological generalization of a celebrated result of Franks from 1992, as conjectured by Hofer and Zehnder in 1994.
Cite
@article{arxiv.1905.04769,
title = {On the Hofer-Zehnder conjecture},
author = {Egor Shelukhin},
journal= {arXiv preprint arXiv:1905.04769},
year = {2019}
}
Comments
54 pages; improvements in exposition, revision of Section 6, results extended to all ground fields