### Abstract

Chaotic scattering is characterized by the existence of nonattracting chaotic invariant sets in phase space. There can be several chaotic invariant sets coexisting in phase space when a system parameter value is below some critical value. As the parameter changes through the critical value, stable and unstable foliations of these chaotic invariant sets, which are fractal sets, can become tangent and then cross each other. The first tangency, which provides the linking between chaotic invariant sets, is a crisis in chaotic scattering. Above the crisis, there is an infinite number of such tangencies which keep occurring until the last tangency, above which the stable and unstable foliations cross transversely. As a consequence of this, the fractal dimension of the set of singularities in the scattering function increases in the parameter range determined by the first and the last tangencies. This leads to a proliferation of singularities in the scattering function and, consequently, to an enhancement of chaotic scattering. The phenomenon is investigated by using both simple one-dimensional models and a two-dimensional physical scattering system.

Original language | English (US) |
---|---|

Pages (from-to) | 3761-3770 |

Number of pages | 10 |

Journal | Physical Review E |

Volume | 49 |

Issue number | 5 |

DOIs | |

State | Published - 1994 |

Externally published | Yes |

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### ASJC Scopus subject areas

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

### Cite this

*Physical Review E*,

*49*(5), 3761-3770. https://doi.org/10.1103/PhysRevE.49.3761

**Crisis and enhancement of chaotic scattering.** / Lai, Ying-Cheng; Grebogi, Celso.

Research output: Contribution to journal › Article

*Physical Review E*, vol. 49, no. 5, pp. 3761-3770. https://doi.org/10.1103/PhysRevE.49.3761

}

TY - JOUR

T1 - Crisis and enhancement of chaotic scattering

AU - Lai, Ying-Cheng

AU - Grebogi, Celso

PY - 1994

Y1 - 1994

N2 - Chaotic scattering is characterized by the existence of nonattracting chaotic invariant sets in phase space. There can be several chaotic invariant sets coexisting in phase space when a system parameter value is below some critical value. As the parameter changes through the critical value, stable and unstable foliations of these chaotic invariant sets, which are fractal sets, can become tangent and then cross each other. The first tangency, which provides the linking between chaotic invariant sets, is a crisis in chaotic scattering. Above the crisis, there is an infinite number of such tangencies which keep occurring until the last tangency, above which the stable and unstable foliations cross transversely. As a consequence of this, the fractal dimension of the set of singularities in the scattering function increases in the parameter range determined by the first and the last tangencies. This leads to a proliferation of singularities in the scattering function and, consequently, to an enhancement of chaotic scattering. The phenomenon is investigated by using both simple one-dimensional models and a two-dimensional physical scattering system.

AB - Chaotic scattering is characterized by the existence of nonattracting chaotic invariant sets in phase space. There can be several chaotic invariant sets coexisting in phase space when a system parameter value is below some critical value. As the parameter changes through the critical value, stable and unstable foliations of these chaotic invariant sets, which are fractal sets, can become tangent and then cross each other. The first tangency, which provides the linking between chaotic invariant sets, is a crisis in chaotic scattering. Above the crisis, there is an infinite number of such tangencies which keep occurring until the last tangency, above which the stable and unstable foliations cross transversely. As a consequence of this, the fractal dimension of the set of singularities in the scattering function increases in the parameter range determined by the first and the last tangencies. This leads to a proliferation of singularities in the scattering function and, consequently, to an enhancement of chaotic scattering. The phenomenon is investigated by using both simple one-dimensional models and a two-dimensional physical scattering system.

UR - http://www.scopus.com/inward/record.url?scp=0000588160&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000588160&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.49.3761

DO - 10.1103/PhysRevE.49.3761

M3 - Article

AN - SCOPUS:0000588160

VL - 49

SP - 3761

EP - 3770

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

ER -