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Geometry and Topology of Escape. II. Homotopic Lobe Dynamics
Mitchell, K. A. Handley, J. P. Delos, John B. Knudson, Stephen
Mitchell, K. A.
Handley, J. P.
Delos, John B.
Knudson, Stephen
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 end point 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 Δ=D+1" role="presentation" style="display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">Δ=D+1Δ=D+1 iterates after the segment to which it converges, where D" role="presentation" style="display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">��D is the minimum delay time of the complex.
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Date
2003-09-01
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American Institute of Physics
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Physics
DOI
https://doi.org/10.1063/1.1598312