Lyapunov function for cosmological dynamical system

Abstract

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.

Keywords

• Lyapunov function
• First integral
• Dynamical system
• Mathematical cosmology
• 34D23
• 83F05