Geometry and Topology of Escape II: Homotopic Lobe Dynamics

Details Geometry and Topology of Escape II: Homotopic Lobe Dynamics Geometry and Topology of Escape II: Homotopic Lobe Dynamics

2003-07-11

arxiv.org/abs/nlin/0307020v1

Nonlinear Sciences

Chaotic Dynamics

13 pages, 8 figures, to appear in Chaos, second of two papers

Scientific paper

10.1063/1.1598312

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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