Dynamical Systems On Generalised Klein Bottles
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912159596806144 |
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| author | Grindrod, Peter Yim, Ka Man |
| author_facet | Grindrod, Peter Yim, Ka Man |
| contents | We propose a high dimensional generalisation of the standard Klein bottle, going beyond those considered previously. We address the problem of generating continuous scalar fields (distributions) and dynamical systems (flows) on such state spaces, which can provide a rich source of examples for future investigations. We consider a class of high dimensional dynamical systems that model distributed information processing within the human cortex, which may be capable of exhibiting some Klein bottle symmetries. We deploy topological data analytic methods in order to analyse their resulting dynamical behaviour, and suggesting future challenges. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_06215 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dynamical Systems On Generalised Klein Bottles Grindrod, Peter Yim, Ka Man Dynamical Systems General Topology 37B02 We propose a high dimensional generalisation of the standard Klein bottle, going beyond those considered previously. We address the problem of generating continuous scalar fields (distributions) and dynamical systems (flows) on such state spaces, which can provide a rich source of examples for future investigations. We consider a class of high dimensional dynamical systems that model distributed information processing within the human cortex, which may be capable of exhibiting some Klein bottle symmetries. We deploy topological data analytic methods in order to analyse their resulting dynamical behaviour, and suggesting future challenges. |
| title | Dynamical Systems On Generalised Klein Bottles |
| topic | Dynamical Systems General Topology 37B02 |
| url | https://arxiv.org/abs/2411.06215 |