Dynamical system describing cloud of particles in relativistic and non-relativistic framework
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917881245073408 |
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| author | Stańczy, Robert Bors, Dorota |
| author_facet | Stańczy, Robert Bors, Dorota |
| contents | We consider fairly general class of dynamical systems under the assumptions guaranteeing the existence of Lyapunov function around some nontrivial stationary point. Moreover, the existence of heteroclinic trajectory is proved motivated by integrated densities approach to some astrophysical models of self-gravitating particles both in relativistic and non--relativistic frameworks. Finally, with the aid of geometric and topological reasoning we find the upper bounds for this trajectory yielding the critical mass--radius theorem for the astrophysical model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20791 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dynamical system describing cloud of particles in relativistic and non-relativistic framework Stańczy, Robert Bors, Dorota Mathematical Physics Astrophysics of Galaxies Dynamical Systems Primary: 35Q85, 70K05, 85A05, Sec.: 34E15, 37N05 We consider fairly general class of dynamical systems under the assumptions guaranteeing the existence of Lyapunov function around some nontrivial stationary point. Moreover, the existence of heteroclinic trajectory is proved motivated by integrated densities approach to some astrophysical models of self-gravitating particles both in relativistic and non--relativistic frameworks. Finally, with the aid of geometric and topological reasoning we find the upper bounds for this trajectory yielding the critical mass--radius theorem for the astrophysical model. |
| title | Dynamical system describing cloud of particles in relativistic and non-relativistic framework |
| topic | Mathematical Physics Astrophysics of Galaxies Dynamical Systems Primary: 35Q85, 70K05, 85A05, Sec.: 34E15, 37N05 |
| url | https://arxiv.org/abs/2412.20791 |