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Fragility in Cosmology and Astrophysics

Published online by Cambridge University Press:  12 April 2016

R.K. Tavakol*
Affiliation:
School of Mathematical Sciences, Queen Mary and Westfield College, Mile End Road, London E1 4NS, England

Abstract

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The theoretical framework adopted in astrophysics and cosmology, in both modelling and the analysis of the observational data, is often implicitly assumed to be that of structural stability. Here, in view of some of the recent results in dynamical systems theory, it is argued that such a framework cannot be assumed a priori and that the fragility framework may instead turn out to be the appropriate framework for the study of certain phenomena in the astrophysical and the cosmological settings. This is motivated by a number of examples from cosmology and a brief discussion of some of the potential domains of its relevance in astrophysics.

Type
Part V General Celestial Mechanics and Stellar Dynamics
Copyright
Copyright © Nova Science Publishers 1993

References

[1] Andronov, A.A. and Pontryagin, L.S. (1937) Doki. Akad. Nauk. SSSR, 14, 247.Google Scholar
[2] Peixoto, M.M. (1962) Topology, 1, 101.CrossRefGoogle Scholar
[3] Tavakol, R.K. and Ellis, G.F.R. (1988) Phys.Letts. 130A, 217.CrossRefGoogle Scholar
[4] Samle, S. (1967) Bull. AMS, 73, 747.CrossRefGoogle Scholar
[5] Markus, L. and Meyer, K.R. (1974) Memoires AMS, Number 144.Google Scholar
[6] Tavakol, R.K. (1978) Nature, 276, 802.CrossRefGoogle Scholar
[7] Ruzmaikin, A.A. (1985) Solar Phys., 100, 125.CrossRefGoogle Scholar
[8] Weiss, N.O., Cattaneo, F. and Jones, C.A. (1984) Geophys. Astrophys. Fluid Dynamics, 30, 305.CrossRefGoogle Scholar
[9] Cox, S.M. (1990) Phys. Letts. 144A, 325.CrossRefGoogle Scholar
[10] Sparrow, C. (1982) The Lorenz Equation. Springer, New York.Google Scholar
[11] Lifshitz, E.M., Lifshitz, I.M., and Khalatnikov, I.M., (1970) JETP, 59, 322.Google Scholar
[12] Barrow, J.D. (1982) Phys. Rep., 85, 1.CrossRefGoogle Scholar
[13] Burd, A.B., Buric, N. and Tavakol, R.K. (1990) Class. Quantum. Grav. In Press.Google Scholar
[14] Fischer, A.E., Marsden, J.E., and Moncrief, V. (1980). in Essays in General Relativity, Tipler, F.J., ed. (Academic Press, New York).Google Scholar
[15] Barrow, J.D. and Stein-Schabes, (1985) Phys.Rev., D32, 1595.Google Scholar
[16] Demaret, J., Hanquin, J.-L., Henneaux, M., Spindel, P. and Taormina, A. (1986) Phys.Letts. 175B, 129.CrossRefGoogle Scholar
[17] Wolf, C. (1988) Phys. Letts. 127A, 129.CrossRefGoogle Scholar
[18] Farina-Busto, L. and Tavakol, R.K. (1990): ‘An Example of Structural Fragility in Cosmology’, Europhysical Letts., 11, 493497.CrossRefGoogle Scholar