Entropy potential and Lyapunov exponents

Details Entropy potential and Lyapunov exponents Entropy potential and Lyapunov exponents

1997-06-03

arxiv.org/abs/chao-dyn/9706004v1

Nonlinear Sciences

Chaotic Dynamics

20 pages, latex, 8 figures, submitted to CHAOS

Scientific paper

10.1063/1.166268

According to a previous conjecture, spatial and temporal Lyapunov exponents of chaotic extended systems can be obtained from derivatives of a suitable function: the entropy potential. The validity and the consequences of this hypothesis are explored in detail. The numerical investigation of a continuous-time model provides a further confirmation to the existence of the entropy potential. Furthermore, it is shown that the knowledge of the entropy potential allows determining also Lyapunov spectra in general reference frames where the time-like and space-like axes point along generic directions in the space-time plane. Finally, the existence of an entropy potential implies that the integrated density of positive exponents (Kolmogorov-Sinai entropy) is independent of the chosen reference frame.

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