Sporadically Fractal Basin Boundaries of Chaotic Systems

Journal Article · Sat May 01 00:00:00 EDT 1999 · Physical Review Letters

DOI:https://doi.org/10.1103/PhysRevLett.82.3597· OSTI ID:337565

Hunt, B R; Ott, E ^[1]; Rosa, E Jr ^[2]

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1. University of Maryland, College Park, Maryland 20742 (United States)
2. Nonlinear Dynamics Laboratory, Department of Physics, University of Miami, Coral Gables, Florida 33146 (United States)

We demonstrate a new type of basin boundary for typical chaotic dynamical systems. For the case of a two dimensional map, this boundary has the character of the graph of a function that is smooth and differentiable except on a set of fractal dimensions less than one. In spite of the basin boundary being smooth {open_quotes}almost everywhere,{close_quotes} its fractal dimension exceeds one (implying degradation of one{close_quote}s ability to predict the attractor an orbit approaches in the presence of small initial condition uncertainty). We call such a boundary {ital sporadically fractal}. {copyright} {ital 1999} {ital The American Physical Society}

• OSTI ID: 337565
• Journal Information: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 18 Vol. 82; ISSN 0031-9007; ISSN PRLTAO
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
DYNAMICS
FRACTALS
PHASE SPACE
SET THEORY