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arXiv · 2312.13840

One Dimensional Dynamics and the R\"ossler attractor

Eran Igra
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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, $x^2+c$, $-2\leq c\leq\frac{1}{4}$.

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Eran Igra. 2023-12-21. One Dimensional Dynamics and the R\"ossler attractor. https://arxiv.org/abs/2312.13840

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