Interacting Geodesics on Discrete Manifolds
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909648953540608 |
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| author | Knill, Oliver |
| author_facet | Knill, Oliver |
| contents | We define an evolution of multiple particles on a discrete manifold $G$. Each particle alone moves on geodesics and particles can interact if they are on the same facet. They move deterministically and reversibly on the frame bundle $P$ of the abstract simplicial complex $G$. Particles are signed and each is represented by a totally ordered maximal simplex $p \in P$ in $G$. The motion of divisors on $P$ also defines a time dependent reversible deformation of space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_12054 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Interacting Geodesics on Discrete Manifolds Knill, Oliver Dynamical Systems Discrete Mathematics Mathematical Physics 55U10, 37B15 We define an evolution of multiple particles on a discrete manifold $G$. Each particle alone moves on geodesics and particles can interact if they are on the same facet. They move deterministically and reversibly on the frame bundle $P$ of the abstract simplicial complex $G$. Particles are signed and each is represented by a totally ordered maximal simplex $p \in P$ in $G$. The motion of divisors on $P$ also defines a time dependent reversible deformation of space. |
| title | Interacting Geodesics on Discrete Manifolds |
| topic | Dynamical Systems Discrete Mathematics Mathematical Physics 55U10, 37B15 |
| url | https://arxiv.org/abs/2506.12054 |