2012/09/01 by G. RUIZ, T. BOUNTIS, C. TSALLIS
Physics and Astronomy · Mathematics · #Statistical Mechanics and Entropy #Theoretical and Computational Physics #Mathematical Dynamics and Fractals
paper · doi:10.1142/s0218127412502082
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.