One Dimensional Dynamics and the Rössler attractor
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913365482274816 |
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| author | Igra, Eran |
| author_facet | Igra, Eran |
| contents | The Rössler 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 Rössler 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, $x^2+c$, $-2\leq c\leq\frac{1}{4}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_13840 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | One Dimensional Dynamics and the Rössler attractor Igra, Eran Dynamical Systems Mathematical Physics Classical Analysis and ODEs The Rössler 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 Rössler 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, $x^2+c$, $-2\leq c\leq\frac{1}{4}$. |
| title | One Dimensional Dynamics and the Rössler attractor |
| topic | Dynamical Systems Mathematical Physics Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2312.13840 |