Essential dynamics in chaotic attractors
Dynamical Systems
2025-01-31 v2 Classical Analysis and ODEs
Abstract
We prove that if a smooth vector field of generates a sufficiently complicated heteroclinic knot, the flow also generates infinitely many periodic orbits, which persist under smooth perturbations which preserve the heteroclinic knot. Consequentially, we then associate a Template with the flow dynamics - regardless of whether satisfies any hyperbolicity condition or not. In addition, inspired by the Thurston-Nielsen Classification Theorem, we also conclude topological criteria for the existence of chaotic dynamics for three-dimensional flows - which we apply to study both the R\"ossler and Lorenz attractors.
Cite
@article{arxiv.2411.08571,
title = {Essential dynamics in chaotic attractors},
author = {Eran Igra},
journal= {arXiv preprint arXiv:2411.08571},
year = {2025}
}