Topology of high-dimensional chaotic scattering

Ying-Cheng Lai, Alessandro P S De Moura, Celso Grebogi

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

We investigate Hamiltonian chaotic scattering in physically realistic three-dimensional potentials. We find that the basin topology of the scattering dynamics can undergo a metamorphosis from being totally disconnected to being connected as a system parameter, such as the particle energy, is varied through a critical value. The dynamical origin of the metamorphosis is investigated, and the topological change in the scattering basin is explained in terms of the change in the structure of the invariant set of nonescaping orbits. A dynamical consequence of this metamorphosis is that the fractal dimension of the chaotic set responsible for the chaotic scattering changes its behavior characteristically at the metamorphosis. This topological metamorphosis has no correspondence in two-degree-of-freedom open Hamiltonian systems.

Original languageEnglish (US)
Pages (from-to)6421-6428
Number of pages8
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume62
Issue number5 B
StatePublished - Nov 2000

Fingerprint

High-dimensional
topology
Scattering
Topology
scattering
Open Systems
Invariant Set
particle energy
Fractal Dimension
Hamiltonian Systems
Critical value
fractals
Correspondence
degrees of freedom
Orbit
Degree of freedom
orbits
Three-dimensional
Energy

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics

Cite this

Topology of high-dimensional chaotic scattering. / Lai, Ying-Cheng; De Moura, Alessandro P S; Grebogi, Celso.

In: Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 62, No. 5 B, 11.2000, p. 6421-6428.

Research output: Contribution to journalArticle

@article{4e670b22b685406ab0fc4d87b46fa6fc,
title = "Topology of high-dimensional chaotic scattering",
abstract = "We investigate Hamiltonian chaotic scattering in physically realistic three-dimensional potentials. We find that the basin topology of the scattering dynamics can undergo a metamorphosis from being totally disconnected to being connected as a system parameter, such as the particle energy, is varied through a critical value. The dynamical origin of the metamorphosis is investigated, and the topological change in the scattering basin is explained in terms of the change in the structure of the invariant set of nonescaping orbits. A dynamical consequence of this metamorphosis is that the fractal dimension of the chaotic set responsible for the chaotic scattering changes its behavior characteristically at the metamorphosis. This topological metamorphosis has no correspondence in two-degree-of-freedom open Hamiltonian systems.",
author = "Ying-Cheng Lai and {De Moura}, {Alessandro P S} and Celso Grebogi",
year = "2000",
month = "11",
language = "English (US)",
volume = "62",
pages = "6421--6428",
journal = "Physical Review E - Statistical, Nonlinear, and Soft Matter Physics",
issn = "1539-3755",
publisher = "American Physical Society",
number = "5 B",

}

TY - JOUR

T1 - Topology of high-dimensional chaotic scattering

AU - Lai, Ying-Cheng

AU - De Moura, Alessandro P S

AU - Grebogi, Celso

PY - 2000/11

Y1 - 2000/11

N2 - We investigate Hamiltonian chaotic scattering in physically realistic three-dimensional potentials. We find that the basin topology of the scattering dynamics can undergo a metamorphosis from being totally disconnected to being connected as a system parameter, such as the particle energy, is varied through a critical value. The dynamical origin of the metamorphosis is investigated, and the topological change in the scattering basin is explained in terms of the change in the structure of the invariant set of nonescaping orbits. A dynamical consequence of this metamorphosis is that the fractal dimension of the chaotic set responsible for the chaotic scattering changes its behavior characteristically at the metamorphosis. This topological metamorphosis has no correspondence in two-degree-of-freedom open Hamiltonian systems.

AB - We investigate Hamiltonian chaotic scattering in physically realistic three-dimensional potentials. We find that the basin topology of the scattering dynamics can undergo a metamorphosis from being totally disconnected to being connected as a system parameter, such as the particle energy, is varied through a critical value. The dynamical origin of the metamorphosis is investigated, and the topological change in the scattering basin is explained in terms of the change in the structure of the invariant set of nonescaping orbits. A dynamical consequence of this metamorphosis is that the fractal dimension of the chaotic set responsible for the chaotic scattering changes its behavior characteristically at the metamorphosis. This topological metamorphosis has no correspondence in two-degree-of-freedom open Hamiltonian systems.

UR - http://www.scopus.com/inward/record.url?scp=0034318667&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034318667&partnerID=8YFLogxK

M3 - Article

VL - 62

SP - 6421

EP - 6428

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

SN - 1539-3755

IS - 5 B

ER -