Fractal dimension in dissipative chaotic scattering

Jesus M. Seoane, Miguel A. F. Sanjuan, Ying-Cheng Lai

Research output: Contribution to journalArticle

44 Citations (Scopus)

Abstract

The effect of weak dissipation on chaotic scattering is relevant to situations of physical interest. We investigate how the fractal dimension of the set of singularities in a scattering function varies as the system becomes progressively more dissipative. A crossover phenomenon is uncovered where the dimension decreases relatively more rapidly as a dissipation parameter is increased from zero and then exhibits a much slower rate of decrease. We provide a heuristic theory and numerical support from both discrete-time and continuous-time scattering systems to establish the generality of this phenomenon. Our result is expected to be important for physical phenomena such as the advection of inertial particles in open chaotic flows, among others.

Original languageEnglish
Article number016208
Number of pages6
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Volume76
Issue number1
DOIs
Publication statusPublished - 10 Jul 2007

Keywords

  • Hamiltonian-systems
  • boundaries
  • dynamics
  • saddles
  • motion
  • sphere
  • model

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