One Dimensional Dynamics and the R\"ossler attractor
Dynamical Systems
2024-05-29 v2 Mathematical Physics
Classical Analysis and ODEs
math.MP
Abstract
The R\"ossler system is one of the best known chaotic dynamical systems, generating a chaotic attractor which, by the numerical evidence, arises by a period-doubling route to chaos. In this paper we state and prove a topological criterion for the existence of an attractor for the R\"ossler system - and then analyze the dynamics of the non-wandering set by reducing the flow to the dynamics of a well-known one dimensional model: the Quadratic Family, , .
Keywords
Cite
@article{arxiv.2312.13840,
title = {One Dimensional Dynamics and the R\"ossler attractor},
author = {Eran Igra},
journal= {arXiv preprint arXiv:2312.13840},
year = {2024}
}