Abstract
We study homogeneous and isotropic cosmologies in different gravity theories with one or two fluids and/or one scalar field as matter source. We give a brief review of the basic mathematical formalism of the theory of finite dynamical systems. We write the field equations in a form suitable for the dynamical system approach and analyze the general properties of the system of DEs describing the evolution of the models. Finally we discuss without technical details the dynamical system approach to the study of Bianchi type models.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
L. Perko: Differential Equations and Dynamical Systems, (Springer-Verlag, 1991).
M.W. Hirsh and S. Smale: Differential Equations, Dynamical Systems and Linear Algebra, (Academic Press, New York, 1974).
J. Wainwright: Relativistic Cosmology In Proceedings of the 46th Scottish Universities Summer School in Physics, Aberdeen, pp. 107–141 Eds G.S. Hall and J.R. Pulham (Institute of Physics Publishing, 1996).
A.A. Coley and J. Wainwright: Class. Quant. Grav. 9, (1992), 651.
R. d’Inverno: Introducing Einstein’s Relativity, (Oxford University Press, 1992)
R.M. Wald: Phys. Rev. D28, (1983), 2118.
J.D. Barrow: Phys. Rev. D48, (1993), 3592.
C. Brans and R.H. Dicke: Phys. Rev. 124, (1961), 925.
D. Holden and D. Wands: Class. Quant. Grav. 15, (1998), 3271.
S. Kolitch and D. Eardley: Annals Phys. 241, (1995), 128.
V.V. Nemytskii and V.V. Stepanov: Qualitative Theory of Differential Equations, (Dover republication of the work first published by Princeton University Press, 1960).
J. Wainwright and G.F.R. Ellis: Dynamical Systems in Cosmology, (Cambridge University Press, 1997).
O.I. Bogoyavlensky: Methods in the Qualitative Theory of Dynamical Systems in Astrophysics and Gas Dynamics, (Springer-Verlag, 1985).
C.B. Collins and S.W. Hawking: Astrophys. J. 180, (1973), 317.
L.D. Landau and E.M. Lifshitz: The Classical Theory of Fields, (Pergamon Press, 4th edition, 1975).
E. Gunzig et al: Class. Quant. Grav. 17, (2000), 1783.
A.A. Coley: gr-qc/9910074 (1999).
S. Foster: Class. Quant. Grav. 15, (1998), 3485.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Miritzis, J. (2002). Introduction to Cosmological Dynamical Systems. In: Cotsakis, S., Papantonopoulos, E. (eds) Cosmological Crossroads. Lecture Notes in Physics, vol 592. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48025-0_6
Download citation
DOI: https://doi.org/10.1007/3-540-48025-0_6
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43778-9
Online ISBN: 978-3-540-48025-9
eBook Packages: Springer Book Archive