Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Lyapunov function for cosmological dynamical system

Lyapunov function for cosmological dynamical system AbstractWe 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.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

Lyapunov function for cosmological dynamical system

Szydłowski, Marek; Krawiec, Adam
Demonstratio Mathematica , Volume 50 (1): 5 – Apr 25, 2017
Download PDF
5 pages

Loading next page...
 
/lp/de-gruyter/lyapunov-function-for-cosmological-dynamical-system-9AiCzy53jK

References

References for this paper are not available at this time. We will be adding them shortly, thank you for your patience.

Publisher
de Gruyter
Copyright
© 2017 Marek Szydłowski and Adam Krawiec
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-2017-0005
Publisher site
See Article on Publisher Site

Abstract

AbstractWe 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.

Journal

Demonstratio Mathematica – de Gruyter

Published: Apr 25, 2017

References

  • generation and the survival of protogalaxies in an expanding universe
    Weinberg
  • The University of Chicago Chicago
    Wald
  • Structural stability properties of and
    Szydłowski
  • Imperfect fluid Friedmannian and Space
    Heller
  • equations dynamical systems rd ed New York
    Perko
  • Influence of viscosity on the character of cosmological evolution
    Belinskii
  • nonintegrability of dynamical systems World Scientific Singapore
    Goriely