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Bianchi Cosmologies as Dynamical Systems

Published online by Cambridge University Press:  12 April 2016

Andrzej J. Maciejewski  and
Marek Szydłowski
Andrzej J. Maciejewski
Affiliation:
Toruń Centre for Astronomy, N. Copernicus University, Chopina 12/18, 87-100 Toruń, Poland; E-mail:maciejka@astri.uni.torun.pl
Marek Szydłowski
Affiliation:
Astronomical Observatory, Jagiellonian University, Orla 171, 30-244 Kraków, Poland; E-mail:uoszydlo@cyf-kr.edu.pl

Abstract

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We discuss specific properties of dynamical systems originating from cosmology and relativity. In particular, we present results of our study of the Bianchi class A cosmological models. We introduce new variables in which the Hamiltonian constraint for all the class A models is solved algebraically. We present results of dimension reduction of the investigated models.

Type
Cosmology
Information
International Astronomical Union Colloquium , Volume 172: Impact of Modern Dynamics in Astronomy , 1999 , pp. 17 - 24
Copyright
Copyright © Kluwer 1999

References

Landau, L.D. and Lifshitz, E.M.: 1975, The Classical Theory of Fields. Pergamon, Oxford.Google Scholar
Wainwright, J. and Ellis, G.F.R.: 1997, Dynamical Systems in Cosmology, Cambridge, U.P., Cambridge.CrossRefGoogle Scholar
Collins, C.B.: 1971 Commun. Math. Phys., 23, 137 (1971).CrossRefGoogle Scholar
Bogoyavlensky, O.I.: 1985, Methods in Qualitative Theory of Dynamical Systems in Astrophysics and Gas Dynamics. New York, Springer-Verlag.Google Scholar
Wainwright, J. and Hsu, L.: 1989 Class. Quantum Grav., 6, 1409.CrossRefGoogle Scholar
Chernoff, D.F. and Barrow, J.D.: 1983, Phys. Rev. Lett., 20, (1983), 134–137.CrossRefGoogle Scholar
Cushman, R. and Śniatycki, J.: 1995, Preprint Univ. of Calgary,.Google Scholar
Cornish, N.J.: 1997, in Proceedings of Eight M. Grossmann Meeting, Jerusalem.Google Scholar
Cornish, N.J. and Levin, J.J.: 1997, in Proceedings of Eight M. Grossmann Meeting, Jerusalem.Google Scholar
Ramani, A., Grammaticos, B. and Bountis, T.: 1989, Phys. Reports 180, 159–254.CrossRefGoogle Scholar
Contopoulos, G., Grammaticos, B. and Ramani, A.: 1993, J. Phys., A26, 5795.Google Scholar
Contopoulos, G., Grammaticos, B. and Ramani, A.: 1994, J. Phys. A, 27, 5357–5361.CrossRefGoogle Scholar
Latifi, A.,Musette, M. and Conte, R.: 1995, Phys. Lett. A, 194, 83–97.CrossRefGoogle Scholar
Contopoulos, G., Grammaticos, B. and Ramani, A.: 1995, J. Phys. A, 28, 5313–5322.CrossRefGoogle Scholar
Morales-Ruiz, J.J. and Ramis, J.-P.: 1997, Galoisian Obstruction to Integrability of Hamiltonian Systems I, II, Preprint.Google Scholar
Belinskii, V. A., Khalatnikov, I.M. and Lifshitz, E. M.: 1982, Adv. Phys., 31, 639.CrossRefGoogle Scholar
Maciejewski, A. J. and Szydłowski, M.: 1998, J. Phys. A. Math. & Gen., 31, 2031.CrossRefGoogle Scholar