Nusse HE, Yorke JA. Fractal basin boundaries generated by basin cells and the geometry of mixing chaotic flows.
PHYSICAL REVIEW LETTERS 2000;
84:626-629. [PMID:
11017332 DOI:
10.1103/physrevlett.84.626]
[Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/30/1999] [Indexed: 05/23/2023]
Abstract
Experiments and computations indicate that mixing in chaotic flows generates certain coherent spatial structures. If a two-dimensional basin has a basin cell (a trapping region whose boundary consists of pieces of the stable and unstable manifold of some periodic orbit) then the basin consists of a central body (the basin cell) and a finite number of channels attached to it and the basin boundary is fractal. We demonstrate an amazing property for certain global structures: A basin has a basin cell if and only if every diverging curve comes close to every basin boundary point of that basin.
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