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Geometry and Topology of Escape II: Homotopic Lobe Dynamics

K. A. Mitchell·J. P. Handley·S. K. Knudson·J. B. Delos
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Abstract

We continue our study of the fractal structure of escape-time plots for chaotic maps. In the preceding paper, we showed that the escape-time plot contains regular sequences of successive escape segments, called epistrophes, which converge geometrically upon each endpoint of every escape segment. In the present paper, we use topological techniques to: (1) show that there exists a minimal required set of escape segments within the escape-time plot; (2) develop an algorithm which computes this minimal set; (3) show that the minimal set eventually displays a recursive structure governed by an ``Epistrophe Start Rule'': a new epistrophe is spawned Delta = D+1 iterates after the segment to which it converges, where D is the minimum delay time of the complex.

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K. A. Mitchell, J. P. Handley, S. K. Knudson, J. B. Delos. 2003-07-11. Geometry and Topology of Escape II: Homotopic Lobe Dynamics. https://doi.org/10.1063/1.1598312

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