Generalization of the Kolmogorov-Sinai entropy: Logistic-like and generalized cosine maps at the chaos threshold

Ugur Tirnakli, Garin F.J. Ananos, Constantino Tsallis

Resultado de la investigación: Contribución a una revistaArtículorevisión exhaustiva

40 Citas (Scopus)

Resumen

We numerically calculate, at the edge of chaos, the time evolution of the nonextensive entropic form Sq ≡ [1 - Σi=1W piq]/[q - 1] (with S1 = - Σi=1W Pi 1n pi) for two families of one-dimensional dissipative maps, namely a logistic-like and a generalized cosine with arbitrary inflexion z at their maximum. At t = 0 we choose N initial conditions inside one of the W small windows in which the accessible phase space is partitioned; to neutralize large fluctuations we conveniently average over a large amount of initial windows. We verify that one and only one value q* < 1 exists such that the limt→∞ limW→∞ limN→∞ Sq (t)/t is finite, thus generalizing the (ensemble version of the) Kolmogorov-Sinai entropy (which corresponds to q* = 1 in the present formalism). This special, z-dependent, value q* numerically coincides, for both families of maps and all z, with the one previously found through two other independent procedures (sensitivity to the initial conditions and multifractal f(α) function).

Idioma originalInglés
Páginas (desde-hasta)51-58
Número de páginas8
PublicaciónPhysics Letters, Section A: General, Atomic and Solid State Physics
Volumen289
N.º1-2
DOI
EstadoPublicada - 8 oct. 2001

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