### Abstract

The method of stabilizing unstable periodic orbits in chaotic dynamical systems by Ott, Grebogi, and Yorke (OGY) is applied to control chaotic scattering in Hamiltonian systems. In particular, we consider the case of nonhyperbolic chaotic scattering, where there exist Kolmogorov-Arnold-Moser (KAM) surfaces in the scattering region. It is found that for short unstable periodic orbits not close to the KAM surfaces, both the probability that a particle can be controlled and the average time to achieve control are determined by the initial exponential decay rate of particles in the hyperbolic component. For periodic orbits near the KAM surfaces, due to the stickiness effect of the KAM surfaces on particle trajectories, the average time to achieve control can greatly exceed that determined by the hyperbolic component. The applicability of the OGY method to stabilize intermediate complexes of classical scattering systems is suggested.

Original language | English |
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Pages (from-to) | 709-717 |

Number of pages | 9 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 48 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1993 |

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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 - Statistical, Nonlinear, and Soft Matter Physics*,

*48*(2), 709-717. https://doi.org/10.1103/PhysRevE.48.709

**Stabilizing chaotic-scattering trajectories using control.** / Lai, Ying Cheng; Tél, T.; Grebogi, Celso.

Research output: Contribution to journal › Article

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, vol. 48, no. 2, pp. 709-717. https://doi.org/10.1103/PhysRevE.48.709

}

TY - JOUR

T1 - Stabilizing chaotic-scattering trajectories using control

AU - Lai, Ying Cheng

AU - Tél, T.

AU - Grebogi, Celso

PY - 1993

Y1 - 1993

N2 - The method of stabilizing unstable periodic orbits in chaotic dynamical systems by Ott, Grebogi, and Yorke (OGY) is applied to control chaotic scattering in Hamiltonian systems. In particular, we consider the case of nonhyperbolic chaotic scattering, where there exist Kolmogorov-Arnold-Moser (KAM) surfaces in the scattering region. It is found that for short unstable periodic orbits not close to the KAM surfaces, both the probability that a particle can be controlled and the average time to achieve control are determined by the initial exponential decay rate of particles in the hyperbolic component. For periodic orbits near the KAM surfaces, due to the stickiness effect of the KAM surfaces on particle trajectories, the average time to achieve control can greatly exceed that determined by the hyperbolic component. The applicability of the OGY method to stabilize intermediate complexes of classical scattering systems is suggested.

AB - The method of stabilizing unstable periodic orbits in chaotic dynamical systems by Ott, Grebogi, and Yorke (OGY) is applied to control chaotic scattering in Hamiltonian systems. In particular, we consider the case of nonhyperbolic chaotic scattering, where there exist Kolmogorov-Arnold-Moser (KAM) surfaces in the scattering region. It is found that for short unstable periodic orbits not close to the KAM surfaces, both the probability that a particle can be controlled and the average time to achieve control are determined by the initial exponential decay rate of particles in the hyperbolic component. For periodic orbits near the KAM surfaces, due to the stickiness effect of the KAM surfaces on particle trajectories, the average time to achieve control can greatly exceed that determined by the hyperbolic component. The applicability of the OGY method to stabilize intermediate complexes of classical scattering systems is suggested.

UR - http://www.scopus.com/inward/record.url?scp=0000375805&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000375805&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.48.709

DO - 10.1103/PhysRevE.48.709

M3 - Article

AN - SCOPUS:0000375805

VL - 48

SP - 709

EP - 717

JO - Physical review. E

JF - Physical review. E

SN - 2470-0045

IS - 2

ER -