Lyapunov function for cosmological dynamical system

We prove the asymptotic global stability of the de Sitter solution in the Friedmann-Robertson-Walker conservative and dissipative cosmology. In the proof we construct a Lyapunov function in an exact form and establish its relationship with the first integral of dynamical system determining evolution...

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Bibliographic Details
Published inDemonstratio mathematica Vol. 50; no. 1; pp. 51 - 55
Main Authors Szydłowski, Marek, Krawiec, Adam
Format Journal Article
LanguageEnglish
Published De Gruyter Open 01.04.2017
De Gruyter
Subjects
34D23
83F05
Dynamical system
First integral
Lyapunov function
Mathematical cosmology
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Summary:We prove the asymptotic global stability of the de Sitter solution in the Friedmann-Robertson-Walker conservative and dissipative cosmology. In the proof we construct a Lyapunov function in an exact form and establish its relationship with the first integral of dynamical system determining evolution of the flat Universe. Our result is that de-Sitter solution is asymptotically stable solution for general form of equation of state p = (ρ, H), where dependence on the Hubble function H means that the effect of dissipation are included.
ISSN:2391-4661
2391-4661
DOI:10.1515/dema-2017-0005