Circular-like Maps: Sensitivity to the Initial Conditions, Multifractality and Nonextensivity

Details Circular-like Maps: Sensitivity to the Initial Conditions, Multifractality and Nonextensivity Circular-like Maps: Sensitivity to the Initial Conditions, Multifractality and Nonextensivity

1998-09-10

arxiv.org/abs/cond-mat/9809151v1

Physics

Condensed Matter

Statistical Mechanics

15 pages (revtex), 8 figs

Scientific paper

10.1007/s100510050941

We generalize herein the usual circular map by considering inflexions of arbitrary power $z$, and verify that the scaling law which has been recently proposed [Lyra and Tsallis, Phys.Rev.Lett. 80 (1998) 53] holds for a large range of $z$. Since, for this family of maps, the Hausdorff dimension $d_f$ equals unity for all $z$ values in contrast with the nonextensivity parameter $q$ which does depend on $z$, it becomes clear that $d_f$ plays no major role in the sensitivity to the initial conditions.

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