Priestley duality and representations of recurrent dynamics
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916330431578112 |
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| author | Kalies, William Vandervorst, Robert |
| author_facet | Kalies, William Vandervorst, Robert |
| contents | For an arbitrary dynamical system there is a strong relationship between global dynamics and the order structure of an appropriately constructed Priestley space. This connection provides an order-theoretic framework for studying global dynamics. In the classical setting, the chain recurrent set, introduced by C. Conley, is an example of an ordered Stone space or Priestley space. Priestley duality can be applied in the setting of dynamics on arbitrary topological spaces and yields a notion of Hausdorff compactification of the (chain) recurrent set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_14359 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Priestley duality and representations of recurrent dynamics Kalies, William Vandervorst, Robert Dynamical Systems General Topology 37Bxx, 37B20, 37B30, 06-XX, 06Dxx, 06D50 For an arbitrary dynamical system there is a strong relationship between global dynamics and the order structure of an appropriately constructed Priestley space. This connection provides an order-theoretic framework for studying global dynamics. In the classical setting, the chain recurrent set, introduced by C. Conley, is an example of an ordered Stone space or Priestley space. Priestley duality can be applied in the setting of dynamics on arbitrary topological spaces and yields a notion of Hausdorff compactification of the (chain) recurrent set. |
| title | Priestley duality and representations of recurrent dynamics |
| topic | Dynamical Systems General Topology 37Bxx, 37B20, 37B30, 06-XX, 06Dxx, 06D50 |
| url | https://arxiv.org/abs/2407.14359 |