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Sticky orbits of chaotic Hamiltonian dynamics

  • Dynamics And Chaos
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Chaos, Kinetics and Nonlinear Dynamics in Fluids and Plasmas

Part of the book series: Lecture Notes in Physics ((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.

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Author information

Authors and Affiliations

  1. Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan 30043, Republic of China

    V. Afraimovich

  2. Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, 10012, New York, New York

    G. M. Zaslavsky

  3. Department of Physics, New York University, 2-4 Washington Place, 10003, New York, New York

    G. M. Zaslavsky

Authors
  1. V. Afraimovich
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  2. G. M. Zaslavsky
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Sadruddin Benkadda George M. Zaslavsky

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© 1998 Springer-Verlag

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Afraimovich, V., Zaslavsky, G.M. (1998). Sticky orbits of chaotic Hamiltonian dynamics. In: Benkadda, S., Zaslavsky, G.M. (eds) Chaos, Kinetics and Nonlinear Dynamics in Fluids and Plasmas. Lecture Notes in Physics, vol 511. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0106953

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  • DOI: https://doi.org/10.1007/BFb0106953

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64635-8

  • Online ISBN: 978-3-540-69180-8

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