Geometry and topology of escape. II. Homotopic lobe dynamics

Chaos

Volumn 13, Issue 3, 2003, Pages 892-902

  Mitchell, K A ^a   Handley, J P ^a   Delos, J B ^a   Knudson, S K ^a  

^a The College of William and Mary   (United States)

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EID: 0141566675     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1598312     Document Type: Article

References (35)

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26. 1.
27. Topologically, the boundary of A would be defined as its closure minus its interior and would therefore include the untangled branches of the stable and unstable manifolds. Here, when we say the boundary of A we mean only the outer boundaries of the capture and escape zones as well as the X point.
28. 2(1). The map H is called a homotopy.
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30. n.
31. 0 ends in an escape segment. Depending upon the direction in which we shift this end point, we can either include or exclude this terminal segment from the minimal set. By convention, we shift the end point in the direction which includes the terminal segment. See the examples in Sec. IV.
32. j is minimized.
33. X and that has a well-defined homotopy class in π(A*, α), the homotopy class of A has a (unique) finite reduced expansion in the basis.
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