When is high-dimensional scattering chaos essentially two dimensional? Measuring the product structure of singularities

G. Drótos, C. Jung, T. Tél

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We demonstrate how the area of the enveloping surface of the scattering singularities in a three-degrees-of-freedom (3-dof) system depends on a perturbation parameter controlling the distance from a reducible case. This dependence is monotonic and approximately linear. Therefore it serves as a measure for this distance, which can be extracted from an investigation of the fractal structure. These features are a consequence of the dynamics being governed by normally hyperbolic invariant manifolds. We conclude that typical n-dof chaotic scattering exhibits either structures developing out of a stack of chaotic structures of 2-dof type or hardly any chaotic effects.

Original languageEnglish
Article number056210
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume86
Issue number5
DOIs
Publication statusPublished - Nov 16 2012

Fingerprint

chaos
Chaos
High-dimensional
Scattering
Singularity
products
scattering
fractals
Hyperbolic Manifold
Fractal Structure
degrees of freedom
Parameter Perturbation
Invariant Manifolds
perturbation
Monotonic
Degree of freedom
Demonstrate

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability

Cite this

@article{00218a0ed73a40529e9e2ec7961df53f,
title = "When is high-dimensional scattering chaos essentially two dimensional? Measuring the product structure of singularities",
abstract = "We demonstrate how the area of the enveloping surface of the scattering singularities in a three-degrees-of-freedom (3-dof) system depends on a perturbation parameter controlling the distance from a reducible case. This dependence is monotonic and approximately linear. Therefore it serves as a measure for this distance, which can be extracted from an investigation of the fractal structure. These features are a consequence of the dynamics being governed by normally hyperbolic invariant manifolds. We conclude that typical n-dof chaotic scattering exhibits either structures developing out of a stack of chaotic structures of 2-dof type or hardly any chaotic effects.",
author = "G. Dr{\'o}tos and C. Jung and T. T{\'e}l",
year = "2012",
month = "11",
day = "16",
doi = "10.1103/PhysRevE.86.056210",
language = "English",
volume = "86",
journal = "Physical review. E",
issn = "2470-0045",
publisher = "American Physical Society",
number = "5",

}

TY - JOUR

T1 - When is high-dimensional scattering chaos essentially two dimensional? Measuring the product structure of singularities

AU - Drótos, G.

AU - Jung, C.

AU - Tél, T.

PY - 2012/11/16

Y1 - 2012/11/16

N2 - We demonstrate how the area of the enveloping surface of the scattering singularities in a three-degrees-of-freedom (3-dof) system depends on a perturbation parameter controlling the distance from a reducible case. This dependence is monotonic and approximately linear. Therefore it serves as a measure for this distance, which can be extracted from an investigation of the fractal structure. These features are a consequence of the dynamics being governed by normally hyperbolic invariant manifolds. We conclude that typical n-dof chaotic scattering exhibits either structures developing out of a stack of chaotic structures of 2-dof type or hardly any chaotic effects.

AB - We demonstrate how the area of the enveloping surface of the scattering singularities in a three-degrees-of-freedom (3-dof) system depends on a perturbation parameter controlling the distance from a reducible case. This dependence is monotonic and approximately linear. Therefore it serves as a measure for this distance, which can be extracted from an investigation of the fractal structure. These features are a consequence of the dynamics being governed by normally hyperbolic invariant manifolds. We conclude that typical n-dof chaotic scattering exhibits either structures developing out of a stack of chaotic structures of 2-dof type or hardly any chaotic effects.

UR - http://www.scopus.com/inward/record.url?scp=84870408035&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84870408035&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.86.056210

DO - 10.1103/PhysRevE.86.056210

M3 - Article

VL - 86

JO - Physical review. E

JF - Physical review. E

SN - 2470-0045

IS - 5

M1 - 056210

ER -