Binary Tree Approach to Scaling in Unimodal Maps

Jukka A. Ketoja; Juhani Kurkijarvi

doi:10.1007/bf02186875

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arXiv · chao-dyn/9305002

Binary Tree Approach to Scaling in Unimodal Maps

Jukka A. Ketoja·Juhani Kurkijarvi

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Abstract

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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Jukka A. Ketoja, Juhani Kurkijarvi. 1993-05-06. Binary Tree Approach to Scaling in Unimodal Maps. https://doi.org/10.1007/bf02186875

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