Lyapunov function for cosmological dynamical system

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
Main Authors: Szydłowski Marek, Krawiec Adam
Format: Article
Language:English
Published: De Gruyter 2017-04-01
Series:Demonstratio Mathematica
Subjects:
Lyapunov function
First integral
Dynamical system
Mathematical cosmology
34D23
83F05
Online Access:http://www.degruyter.com/view/j/dema.2017.50.issue-1/dema-2017-0005/dema-2017-0005.xml?format=INT
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spelling doaj-d89a8d4645ee4c40b8be222dd21ab8e52020-11-25T01:31:30ZengDe GruyterDemonstratio Mathematica2391-46612017-04-01501515510.1515/dema-2017-0005dema-2017-0005Lyapunov function for cosmological dynamical systemSzydłowski Marek0Krawiec Adam1Astronomical Observatory, Jagiellonian University, Orla 171, 30-244 Kraków, PolandInstitute of Economics, Finance and Management, Jagiellonian University, Łojasiewicza 4, 30-348 Kraków, PolandWe 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.http://www.degruyter.com/view/j/dema.2017.50.issue-1/dema-2017-0005/dema-2017-0005.xml?format=INTLyapunov functionFirst integralDynamical systemMathematical cosmology34D2383F05
collection DOAJ
language English
format Article
sources DOAJ
author Szydłowski Marek
Krawiec Adam
spellingShingle Szydłowski Marek
Krawiec Adam
Lyapunov function for cosmological dynamical system
Demonstratio Mathematica
Lyapunov function
First integral
Dynamical system
Mathematical cosmology
34D23
83F05
author_facet Szydłowski Marek
Krawiec Adam
author_sort Szydłowski Marek
title Lyapunov function for cosmological dynamical system
title_short Lyapunov function for cosmological dynamical system
title_full Lyapunov function for cosmological dynamical system
title_fullStr Lyapunov function for cosmological dynamical system
title_full_unstemmed Lyapunov function for cosmological dynamical system
title_sort lyapunov function for cosmological dynamical system
publisher De Gruyter
series Demonstratio Mathematica
issn 2391-4661
publishDate 2017-04-01
description 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.
topic Lyapunov function
First integral
Dynamical system
Mathematical cosmology
34D23
83F05
url http://www.degruyter.com/view/j/dema.2017.50.issue-1/dema-2017-0005/dema-2017-0005.xml?format=INT
work_keys_str_mv AT szydłowskimarek lyapunovfunctionforcosmologicaldynamicalsystem
AT krawiecadam lyapunovfunctionforcosmologicaldynamicalsystem
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