Fractal and multifractal properties of exit times and Poincar{acute e} recurrences

Journal Article · Thu May 01 00:00:00 EDT 1997 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

DOI:https://doi.org/10.1103/PhysRevE.55.5418· OSTI ID:656939

Afraimovich, V ^[1]; Zaslavsky, M ^[2]

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1. National Tsing Hua University, Department of Mathematics, Hsinchu, Taiwan 30043, Republic of (China)
2. Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, New York 10012 (United States)

Systems with chaotic dynamics possess anomalous statistical properties, and their trajectories do not correspond to the Gaussian process. This property imposes description of such time characteristics as the distribution of exit times or Poincar{acute e} recurrences by introducing a (multi-) fractal time scale in order to satisfy the observed powerlike tails of the distributions. We introduce a corresponding phase-space-time partitioning and spectral function for dimensions, and make a connection between dimensions and transport exponent that defines the anomalous ({open_quotes}strange{close_quotes}) kinetics. {copyright} {ital 1997} {ital The American Physical Society}

• DOE Contract Number: FG02-92ER54184
• OSTI ID: 656939
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 55, Issue 5; Other Information: PBD: May 1997
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
STOCHASTIC PROCESSES
TRAJECTORIES
HAMILTONIAN FUNCTION
FRACTALS
PHASE SPACE
SPECTRAL FUNCTIONS