Relativity and cosmology
Einstein's theories of special and general relativity have revolutionised
our understanding of space and time, and chaotic dynamics is no exception.
Chaotic instability is usually quantified in terms of Lyapunov exponents,
however these in general depend on the definition of time, which is
general relativity is somewhat arbitrary, so coordinate invariant indicators
such as fractal dimensions are important.
Cosmology is also an important arena for the study of
stochastic stabilisation. In the latter, the
unstable (or neutral) behviour of trajectories in negatively curved (or flat)
spaces is stabilised by curvature fluctuations, for example due to galaxies,
in the same way that an upturned pendulum is stabilised by shaking the pivot.
My relativity lecture course is
- Plasma electrodynamics in the expanding Universe. C. P. Dettmann, N. E. Frankel and V. Kowalenko, Phys. Rev. D 48, 5655-5667 (1993) pdf
- Fractal basins and chaotic trajectories in multi-black-hole space-times. C. P. Dettmann, N. E. Frankel and N. J. Cornish, Phys. Rev. D, 50, R618-R621 (1994) pdf arxiv
- Magnetized plasmas in the early universe R. M. Gailis, C. P. Dettmann, N. E. Frankel and V. Kowalenko, Phys. Rev. D 50,3847-3858 (1994) pdf
- Chaos and fractals around black holes C. P. Dettmann, N. E. Frankel and N. J. Cornish, Fractals 3 161-181 (1995) pdf arxiv
- Magnetohydrodynamics in the expanding Universe R. M. Gailis, C. P. Dettmann and N. E. Frankel, Phys. Rev. D 52, 6901-6917 (1995) pdf (large: 1.2M)
- Chaos in special relativistic dynamics S. Drake, C. P. Dettmann, N. E. Frankel and N. J. Cornish, Phys. Rev. E 53,1351-1361 (1996) pdf
- Stochastic dynamics of relativistic turbulence. C. P. Dettmann and N. E. Frankel, Phys. Rev. E 53, 5502-5505 (1996) pdf
- Stochastic stabilization of cosmological photons. C. P. Dettmann, J. P. Keating, and S. D. Prado, J. Phys. A.: Math. Theor.37 L377-L383 (2004) pdf. arxiv animation (0.3M) [Featured in the June 2010 issue of Mathematics Today, pdf available here.]
- Stochastic stabilization of chaos and the cosmic microwave background. C. P. Dettmann, J. P. Keating and S. D. Prado, Int. J. Mod. Phys. D 13 1461-1468 (2004). pdf
- Conference paper: Stochastic stabilization of the cosmic microwave background radiation, C. P. Dettmann, J. P. Keating and S. D. Prado, Proceedings of the Tenth Marcel Grossmann Meeting on General Relativity, ed M. Novello, S. Perez-Bergliaffa and R. Ruffini, World Scientific, Singapore (2006) ps pdf.
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