Using Erd\H{o}s's methods to study Yorke's problems
Dynamical Systems
2025-09-09 v1 Classical Analysis and ODEs
Combinatorics
Abstract
In this paper, we study the possible bifurcations of periodic orbits by reducing them to graphs. The aforementioned allows to study the genericity of routes to chaos, as well as to analyze their possible complexity. In particular, our results show that there is no upper bound on the possible complexity. Moreover, it suggests general fermionic description via the virial expansion and universal description via the Rado graph.
Cite
@article{arxiv.2509.06852,
title = {Using Erd\H{o}s's methods to study Yorke's problems},
author = {Eran Igra and Valerii Sopin},
journal= {arXiv preprint arXiv:2509.06852},
year = {2025}
}