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Sticky orbits of chaotic Hamiltonian dynamics

  • V. Afraimovich
  • G. M. Zaslavsky
Dynamics And Chaos
Part of the Lecture Notes in Physics book series (LNP, volume 511)

Abstract

Nonuniformity of the phase space of chaotic Hamiltonian dynamics can result from the existence of a sticky set called “Sticky Riddle” (SR) imbedded into the phase space. Fractal and multifractal properties of SR can be described for some simplified situations. Existence of SR imposes similar stickiness for chaotic orbits when they approach the vicinity of SR. As a result, the orbits reveal behavior with power-like tails in the distribution of Poincaré recurrences and exit times, which is unusual for hyperbolic systems. We exploit the generalized fractal dimension to describe the set of recurrences.

Keywords

Chaos fractals dimensions Poincaré recurrences 

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Copyright information

© Springer-Verlag 1998

Authors and Affiliations

  • V. Afraimovich
    • 1
  • G. M. Zaslavsky
    • 2
    • 3
  1. 1.Department of MathematicsNational Tsing Hua UniversityHsinchuTaiwan 30043, Republic of China
  2. 2.Courant Institute of Mathematical SciencesNew York UniversityNew York
  3. 3.Department of PhysicsNew York UniversityNew York

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