Lyapunov function for cosmological dynamical system

• Autorzy: Szydłowski M. , Krawiec A.

Identyfikatory

DOI

10.1515/dema-2017-0005

• Języki publikacji: EN

Abstrakty

EN

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 = p(p, H), where dependence on the Hubble function H means that the effect of dissipation are included.

Słowa kluczowe

EN

Lyapunov function; first integral; dynamical system; mathematical cosmology

PL

funkcja Lyapunova; całka pierwsza; układ dynamiczny; kosmologia matematyczna

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2017
• Tom: Vol. 50, nr 1
• Strony: 51--55
• Opis fizyczny: Bibliogr. 7 poz., wykr.

Twórcy

autor

Szydłowski M.

• Astronomical Observatory, Jagiellonian University, Orla 171, 30-244 Kraków, Poland

autor

Krawiec A.

• Institute of Economics, Finance and Management, Jagiellonian University, Łojasiewicza 4, 30-348 Kraków, Poland

Bibliografia

• [1] Wald R. M., General relativity, The University of Chicago Press, Chicago, 1984
• [2] Weinberg S., Entropy generation and the survival of protogalaxies in an expanding universe, Astrophysical Journal, 1971, 168, 175-194
• [3] Heller M., Klimek Z., Suszycki L., Imperfect fluid Friedmannian cosmology, Astrophysics and Space Science, 1973, 20, 205-212
• [4] Belinskii V. A., Khalatnikov I. M., Influence of viscosity on the character of cosmological evolution, Sov. Phys. JETP, 1975, 42, 205-210
• [5] Szydłowski M., Heller M., Golda Z., Structural stability properties of Friedman cosmology General Relativity and Gravitation, 1984, 16, 877-890
• [6] Perko L., Differential equations and dynamical systems, 3rd ed., Springer, New York, 2001
• [7] Goriely A., Integrability and nonintegrability of dynamical systems, World Scientific, Singapore, 2001

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).