A mechanism for growth of topological entropy and global changes of the shape of chaotic attractors
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866910905300680704 |
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| author | Wilczak, Daniel Serrano, Sergio Barrio, Roberto |
| author_facet | Wilczak, Daniel Serrano, Sergio Barrio, Roberto |
| contents | The theoretical and numerical understanding of the key concept of topological entropy is an important problem in dynamical systems. Most studies have been carried out on maps (discrete-time systems). We analyse a scenario of global changes of the structure of an attractor in continuous-time systems leading to an unbounded growth of the topological entropy of the underlying dynamical system. As an example, we consider the classical Roessler system. We show that for an explicit range of parameters a chaotic attractor exists. We also prove the existence of a sequence of bifurcations leading to the growth of the topological entropy. The proofs are computer-aided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_04887 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A mechanism for growth of topological entropy and global changes of the shape of chaotic attractors Wilczak, Daniel Serrano, Sergio Barrio, Roberto Dynamical Systems Numerical Analysis Chaotic Dynamics 34C23, 34C25, 37A35, 37B10, 37B40 The theoretical and numerical understanding of the key concept of topological entropy is an important problem in dynamical systems. Most studies have been carried out on maps (discrete-time systems). We analyse a scenario of global changes of the structure of an attractor in continuous-time systems leading to an unbounded growth of the topological entropy of the underlying dynamical system. As an example, we consider the classical Roessler system. We show that for an explicit range of parameters a chaotic attractor exists. We also prove the existence of a sequence of bifurcations leading to the growth of the topological entropy. The proofs are computer-aided. |
| title | A mechanism for growth of topological entropy and global changes of the shape of chaotic attractors |
| topic | Dynamical Systems Numerical Analysis Chaotic Dynamics 34C23, 34C25, 37A35, 37B10, 37B40 |
| url | https://arxiv.org/abs/2504.04887 |