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Statistical descriptions of nonlinear systems at the onset of chaos

Massmimo Coraddu·Marcello Lissia·Roberto Tonelli
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Abstract

Ensemble of initial conditions for nonlinear maps can be described in terms of entropy. This ensemble entropy shows an asymptotic linear growth with rate K. The rate K matches the logarithm of the corresponding asymptotic sensitivity to initial conditions λ. The statistical formalism and the equality K=λcan be extended to weakly chaotic systems by suitable and corresponding generalizations of the logarithm and of the entropy. Using the logistic map as a test case we consider a wide class of deformed statistical description which includes Tsallis, Abe and Kaniadakis proposals. The physical criterion of finite-entropy growth K strongly restricts the suitable entropies. We study how large is the region in parameter space where the generalized description is useful.

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Massmimo Coraddu, Marcello Lissia, Roberto Tonelli. 2005-11-30. Statistical descriptions of nonlinear systems at the onset of chaos. https://doi.org/10.1016/j.physa.2006.01.007

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