Using Erd\H{o}s's methods to study Yorke's problems

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.