English

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, x2+cx^2+c, 2c14-2\leq c\leq\frac{1}{4}.

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}
}
R2 v1 2026-06-28T13:58:41.164Z