| Fractals and Symbolic Dynamics as Invariant Descriptors of Chaos in General Relativity (2007) | |||||||||||||
Abstract | |||||||||||||
| coordinate transformation t ! ln ø . In terms of this time variable we find "(ø ) = " 0 ø ; which describes the standard power-law divergence of trajectories found in integrable system. In particular, the Lyapunov exponents in this coordinate system would all be zero. It should be mentioned that the Lyapunov exponents also depend on the choice of distance measure in phase space and are therefore variant under spatial coordinate transformations also. From the above discussion it is clear that standard coordinate dependent measures of chaos have to be either modified, abandoned or augmented in general relativity 2 . This problem has now been solved in a series of papers 3;4;5 which introduced and illustrated the effectiveness of fractal dimensions and symbolic codings as invariant descriptors of chaos in general | |||||||||||||
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