Statistical descriptions of nonlinear systems at the onset of chaos
TONELLI, ROBERTO
2006-01-01
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 l. The statistical formalism and the equality K ¼ l can 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.File | Dimensione | Formato | |
---|---|---|---|
45PhyscaA365a2006p252statDescripOnsetChaos.pdf Solo gestori archivio
Tipologia: versione editoriale
Dimensione 194.77 kB
Formato Adobe PDF
|
194.77 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.