Algorithms and topological invariants for dynamic systems. II. Discrete Structures
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910808512921600 |
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| author | Prishlyak, Alexandr |
| author_facet | Prishlyak, Alexandr |
| contents | We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused basic concepts of diferential topology. In the second part we discus the main discrete topological structures used in the topological theory of dynamic systems: simplicial complexes, regular SW-complexes, Euler characteristic and homology groops, Morse-Smale complexes and handle decomposition of manifolds, Poincare rotation index of vector field, discrete Morse function and vector fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_00506 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Algorithms and topological invariants for dynamic systems. II. Discrete Structures Prishlyak, Alexandr Dynamical Systems Geometric Topology 37c10, 37c15, 37c20 G.1.7 We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused basic concepts of diferential topology. In the second part we discus the main discrete topological structures used in the topological theory of dynamic systems: simplicial complexes, regular SW-complexes, Euler characteristic and homology groops, Morse-Smale complexes and handle decomposition of manifolds, Poincare rotation index of vector field, discrete Morse function and vector fields. |
| title | Algorithms and topological invariants for dynamic systems. II. Discrete Structures |
| topic | Dynamical Systems Geometric Topology 37c10, 37c15, 37c20 G.1.7 |
| url | https://arxiv.org/abs/2502.00506 |