General relativistic chaos and nonlinear dynamics

Details General relativistic chaos and nonlinear dynamics General relativistic chaos and nonlinear dynamics

Jun 1982

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982gregr..14..523b&link_type=abstract

General Relativity and Gravitation, vol. 14, June 1982, p. 523-530.

Physics

9

Chaos, Cosmology, Entropy, Gravitation Theory, Random Processes, Relativistic Theory, Difference Equations, Nonlinear Systems

Scientific paper

It is pointed out that during the last few years applied mathematicians and physicists from a variety of backgrounds have been intensively investigating the onset of chaotic behavior in a wide spectrum of simple deterministic dynamic systems. The meaning of 'chaotic' or 'random' behavior in a deterministic system is discussed, and it is shown that the Einstein equations are chaotic according to the assumed meaning. The spatially homogeneous Mixmaster universe of Bianchi type IX is considered. It is found possible to view the Mixmaster system as a chaotic flow in a two-dimensional phase space which possesses a one-dimensional Poincare return mapping. There exists a function which makes it possible to view the Mixmaster universe as a measureable system. Its metric entropy can be calculated. A 'chaotic cosmology' can be rigorously defined as a solution to Einstein's equation whose dynamics possess a nonzero metric entropy.

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