Decay of the distance autocorrelation and Lyapunov exponents

Mendes, C. F. O.; da Silva, R. M.; Beims, Marcus W.

doi:10.1103/PhysRevE.99.062206

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Decay of the distance autocorrelation and Lyapunov exponents

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Beims, Marcus W.
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Citation

Mendes, C. F. O., da Silva, R. M., & Beims, M. W. (2019). Decay of the distance autocorrelation and Lyapunov exponents. Physical Review E, 99(6): 062206. doi:10.1103/PhysRevE.99.062206.

Cite as: https://hdl.handle.net/21.11116/0000-0004-6F06-A

Abstract

This work presents numerical evidence that for discrete dynamical systems with one positive Lyapunov exponent the decay of the distance autocorrelation is always related to the Lyapunov exponent. Distinct decay laws for the distance autocorrelation are observed for different systems, namely, exponential decays for the quadratic map, logarithmic for the Henon map, and power-law for the conservative standard map. In all these cases the decay exponent is close to the positive Lyapunov exponent. For hyperchaotic conservative systems the power-law decay of the distance autocorrelation is not directly related to any Lyapunov exponent.