Knots and Chaos in the Rössler System
arXiv:2306.04772 · doi:10.1016/j.jde.2025.113290
Abstract
The Rössler System is one of the best known chaotic dynamical systems, exhibiting a plethora of complex phenomena - and yet, only a few studies tackled its complexity analytically. In this paper we find sufficient conditions for the existence of chaotic dynamics for the Rössler System at some specific parameter values at which the flow satisfies a certain heteroclinic condition. This will allow us to prove the existence of infinitely many periodic trajectories for the flow, and study their bifurcations in the parameter space of the Rössler system.