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arXiv · 2411.08571

Essential dynamics in chaotic attractors

Eran Igra
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Abstract

We prove that if a smooth vector field $F$ of $S^3$ 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 $F$ 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.

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Eran Igra. 2024-11-13. Essential dynamics in chaotic attractors. https://arxiv.org/abs/2411.08571

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