### 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 |
---|---|

Pages (from-to) | 3761-3770 |

Number of pages | 10 |

Journal | Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 49 |

Issue number | 5 |

Publication status | Published - May 1994 |

### Keywords

- BIFURCATION
- ATTRACTORS
- BEHAVIOR

### Cite this

*Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*,

*49*(5), 3761-3770.

**CRISIS AND ENHANCEMENT OF CHAOTIC SCATTERING.** / LAI, Y C ; GREBOGI, C ; Lai, Ying-Cheng.

Research output: Contribution to journal › Article

*Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*, vol. 49, no. 5, pp. 3761-3770.

}

TY - JOUR

T1 - CRISIS AND ENHANCEMENT OF CHAOTIC SCATTERING

AU - LAI, Y C

AU - GREBOGI, C

AU - Lai, Ying-Cheng

PY - 1994/5

Y1 - 1994/5

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.

KW - BIFURCATION

KW - ATTRACTORS

KW - BEHAVIOR

M3 - Article

VL - 49

SP - 3761

EP - 3770

JO - Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1063-651X

IS - 5

ER -