Dynamical system describing cloud of particles in relativistic and non-relativistic framework
DOI:
https://doi.org/10.12775/TMNA.2026.007Słowa kluczowe
Dynamical system, Lyapunov function, Einstein equation, TOV model, Smoluchowski-Poisson equation, general relativityAbstrakt
We consider a fairly general class of dynamical systems under assumptions that guarantee the existence of a Lyapunov function around a nontrivial stationary point. Moreover, we prove the existence of a heteroclinic trajectory. Finally, using geometric and topological reasoning, we establish an upper bound for this trajectory. The results can be interpreted as limit theorems in terms of integrated densities for astrophysical models in both relativistic and classical frameworks. These models encompass the static Smoluchowski-Poisson and Tolman-Oppenheimer-Volkoff equations.Bibliografia
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Prawa autorskie (c) 2026 Robert Stańczy, Dorota Bors
Utwór dostępny jest na licencji Creative Commons Uznanie autorstwa – Bez utworów zależnych 4.0 Międzynarodowe.
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