The random Arnold Conjecture: a new probabilistic Conley-Zehnder Theory for symplectic maps
Abstract
We take the first steps to develop Conley-Zehnder Theory, as conjectured by Arnold, in the world of probability. As far as we know, this paper provides the first probabilistic theorems about the density of fixed points of symplectic twist maps in dimensions greater than . In particular we will show that, when the analogue conditions to classical Conley-Zehnder theory hold, quasiperiodic symplectic twist maps have infinitely many fixed points almost surely. The paper contains also a number of theorems which go well beyond the quasiperiodic case.
Keywords
Cite
@article{arxiv.2306.15586,
title = {The random Arnold Conjecture: a new probabilistic Conley-Zehnder Theory for symplectic maps},
author = {Álvaro Pelayo and Fraydoun Rezakhanlou},
journal= {arXiv preprint arXiv:2306.15586},
year = {2023}
}
Comments
54 pages. Some partial results have been strengthened, overall presentation improved, several examples and connections with other subjects have been added and made explicit, further motivations included