Fractal dimension in nonhyperbolic chaotic scattering

Journal Article · Sun Feb 24 23:00:00 EST 1991 · Physical Review Letters; (USA)

DOI:https://doi.org/10.1103/PhysRevLett.66.978· OSTI ID:5909071

Lau, Y; Finn, J M; Ott, E ^[1]

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1. Laboratory for Plasma Research, University of Maryland, College Park, Maryland 20742-3511 (US)

In chaotic scattering there is a Cantor set of input-variable values of zero Lebesgue measure (i.e., zero total length) on which the scattering function is singular. For cases where the dynamics leading to chaotic scattering is nonhyperbolic (e.g., there are Kolmogorov-Arnol'd-Moser tori), the nature of this singular set is fundamentally different from that in the hyperbolic case. In particular, for the nonhyperbolic case, although the singular set has zero total length, we present strong evidence that its fractal dimension is 1.

• OSTI ID: 5909071
• Journal Information: Physical Review Letters; (USA), Journal Name: Physical Review Letters; (USA) Vol. 66:8; ISSN PRLTA; ISSN 0031-9007
• Country of Publication: United States
• Language: English

Related Subjects

645201* -- High Energy Physics-- Particle Interactions & Properties-Theoretical-- General & Scattering Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
DYNAMICS
FRACTALS
HAMILTONIANS
MAPPING
MATHEMATICAL OPERATORS
MECHANICS
NUMERICAL SOLUTION
PARAMETRIC ANALYSIS
QUANTUM OPERATORS
SCATTERING