Binary Tree Approach to Scaling in Unimodal Maps

Details Binary Tree Approach to Scaling in Unimodal Maps Binary Tree Approach to Scaling in Unimodal Maps

1993-05-06

arxiv.org/abs/chao-dyn/9305002v1

Nonlinear Sciences

Chaotic Dynamics

25 pages, plain TeX

Scientific paper

10.1007/BF02186875

Ge, Rusjan, and Zweifel (J. Stat. Phys. 59, 1265 (1990)) introduced a binary tree which represents all the periodic windows in the chaotic regime of iterated one-dimensional unimodal maps. We consider the scaling behavior in a modified tree which takes into account the self-similarity of the window structure. A non-universal geometric convergence of the associated superstable parameter values towards a Misiurewicz point is observed for almost all binary sequences with periodic tails. There are an infinite number of exceptional sequences, however, which lead to superexponential scaling. The origin of such sequences is explained.

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