TY - JOUR

T1 - Time-evolving statistics of chaotic orbits of conservative maps in the context of the central limit theorem

AU - Ruiz, G.

AU - Bountis, T.

AU - Tsallis, C.

N1 - Funding Information:
T. Bountis is grateful for the hospitality of the Centro Brasileiro de Pesquisas Fisicas, at Rio de Janeiro, during March 1–April 5, 2010, where part of the work reported here was carried out. We acknowledge partial financial support by CNPq, Capes and Faperj (Brazilian Agencies) and DGU-MEC (Spanish Ministry of Education) through Project PHB2007-0095-PC.

PY - 2012/9

Y1 - 2012/9

N2 - We study chaotic orbits of conservative low-dimensional maps and present numerical results showing that the probability density functions (pdfs) of the sum of N iterates in the large N limit exhibit very interesting time-evolving statistics. In some cases where the chaotic layers are thin and the (positive) maximal Lyapunov exponent is small, long-lasting quasi-stationary states (QSS) are found, whose pdfs appear to converge to q-Gaussians associated with nonextensive statistical mechanics. More generally, however, as N increases, the pdfs describe a sequence of QSS that pass from a q-Gaussian to an exponential shape and ultimately tend to a true Gaussian, as orbits diffuse to larger chaotic domains and the phase space dynamics becomes more uniformly ergodic.

AB - We study chaotic orbits of conservative low-dimensional maps and present numerical results showing that the probability density functions (pdfs) of the sum of N iterates in the large N limit exhibit very interesting time-evolving statistics. In some cases where the chaotic layers are thin and the (positive) maximal Lyapunov exponent is small, long-lasting quasi-stationary states (QSS) are found, whose pdfs appear to converge to q-Gaussians associated with nonextensive statistical mechanics. More generally, however, as N increases, the pdfs describe a sequence of QSS that pass from a q-Gaussian to an exponential shape and ultimately tend to a true Gaussian, as orbits diffuse to larger chaotic domains and the phase space dynamics becomes more uniformly ergodic.

KW - Central limit theorem

KW - Conservative maps

KW - Dynamical systems

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U2 - 10.1142/S0218127412502082

DO - 10.1142/S0218127412502082

M3 - Article

AN - SCOPUS:84867556877

VL - 22

JO - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

JF - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

SN - 0218-1274

IS - 9

M1 - 1250208

ER -