The $E$-cohomological Conley Index, Cup-Lengths and the Arnold Conjecture on $T^{2n}$
Dynamical Systems
2017-09-01 v1 Classical Analysis and ODEs
Symplectic Geometry
Abstract
We give a new proof of the strong Arnold conjecture for -periodic solutions of Hamiltonian systems on tori, that was first shown by C. Conley and E. Zehnder in 1983. Our proof uses other methods and is shorter than the previous one. We first show that the -cohomological Conley index, that was introduced by the first author recently, has a natural module structure. This yields a new cup-length and a lower bound for the number of critical points of functionals. Then an existence result for the -cohomological Conley index, which applies to the setting of the Arnold conjecture, paves the way to a new proof of it on tori.
Keywords
Cite
@article{arxiv.1708.09631,
title = {The $E$-cohomological Conley Index, Cup-Lengths and the Arnold Conjecture on $T^{2n}$},
author = {Maciej Starostka and Nils Waterstraat},
journal= {arXiv preprint arXiv:1708.09631},
year = {2017}
}
Comments
15 pages, 1 figure