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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2504.02635 |
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| _version_ | 1866917977318752256 |
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| author | Posadskiy, Konstantin M. |
| author_facet | Posadskiy, Konstantin M. |
| contents | We study continuous 2-valued dynamical systems with discrete time (dynamics) on $\mathbb{C}$. The main question addressed is whether a 2-valued dynamics can be defined by the action of a 2-valued group. We construct a class of strongly invertible continuous 2-valued dynamics on $\mathbb{C}$ such that none of these dynamics can be given by the action of any 2-valued group. We also construct an example of a continuous 2-valued dynamics on $\mathbb{C}$ that is not strongly invertible but can be defined by the action of a 2-valued group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_02635 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Continuous two-valued discrete-time dynamical systems and actions of two-valued groups Posadskiy, Konstantin M. Group Theory Dynamical Systems Geometric Topology We study continuous 2-valued dynamical systems with discrete time (dynamics) on $\mathbb{C}$. The main question addressed is whether a 2-valued dynamics can be defined by the action of a 2-valued group. We construct a class of strongly invertible continuous 2-valued dynamics on $\mathbb{C}$ such that none of these dynamics can be given by the action of any 2-valued group. We also construct an example of a continuous 2-valued dynamics on $\mathbb{C}$ that is not strongly invertible but can be defined by the action of a 2-valued group. |
| title | Continuous two-valued discrete-time dynamical systems and actions of two-valued groups |
| topic | Group Theory Dynamical Systems Geometric Topology |
| url | https://arxiv.org/abs/2504.02635 |