Removable dynamics in the Nose-Hoover and Moore-Spiegel Oscillators
Dynamical Systems
2025-04-01 v3 Mathematical Physics
Classical Analysis and ODEs
math.MP
Abstract
We study the dynamics of the Nose-Hoover and Moore-Spiegel Oscillators, and in particular, their topological dynamics. We prove the dynamics of both these systems can be reduced to a flow on a solid torus, with at most a finite number of attracting periodic trajectories. As a consequence, we obtain that every periodic trajectory for the Nose-Hoover and the Moore-Spiegel Oscillators is a Torus knot.
Keywords
Cite
@article{arxiv.2409.16624,
title = {Removable dynamics in the Nose-Hoover and Moore-Spiegel Oscillators},
author = {Eran Igra},
journal= {arXiv preprint arXiv:2409.16624},
year = {2025}
}
Comments
I found a mistake in both main theorems