### Abstract

An outstanding problem in chaotic dynamics is to specify generating partitions for symbolic dynamics in dimensions larger than 1. It has been known that the infinite number of unstable periodic orbits embedded in the chaotic invariant set provides sufficient information for estimating the generating partition. Here we present a general, dimension-independent, and efficient approach for this task based on optimizing a set of proximity functions defined with respect to periodic orbits. Our algorithm allows us to obtain the approximate location of the generating partition for the Ikeda-Hammel-Jones-Moloney map.

Original language | English |
---|---|

Pages (from-to) | 1353-1356 |

Number of pages | 4 |

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

Volume | 61 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1 Feb 2000 |

### Keywords

- symbolic dynamics
- strange attractor
- ring cavity
- henon map

### Cite this

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

*61*(2), 1353-1356. https://doi.org/10.1103/PhysRevE.61.1353

**Estimating generating partitions of chaotic systems by unstable periodic orbits.** / Davidchack, Ruslan L.; Lai, Ying-Cheng; Bollt, Erik M. ; Dhamala, Mukeshwar.

Research output: Contribution to journal › Article

*Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*, vol. 61, no. 2, pp. 1353-1356. https://doi.org/10.1103/PhysRevE.61.1353

}

TY - JOUR

T1 - Estimating generating partitions of chaotic systems by unstable periodic orbits

AU - Davidchack, Ruslan L.

AU - Lai, Ying-Cheng

AU - Bollt, Erik M.

AU - Dhamala, Mukeshwar

PY - 2000/2/1

Y1 - 2000/2/1

N2 - An outstanding problem in chaotic dynamics is to specify generating partitions for symbolic dynamics in dimensions larger than 1. It has been known that the infinite number of unstable periodic orbits embedded in the chaotic invariant set provides sufficient information for estimating the generating partition. Here we present a general, dimension-independent, and efficient approach for this task based on optimizing a set of proximity functions defined with respect to periodic orbits. Our algorithm allows us to obtain the approximate location of the generating partition for the Ikeda-Hammel-Jones-Moloney map.

AB - An outstanding problem in chaotic dynamics is to specify generating partitions for symbolic dynamics in dimensions larger than 1. It has been known that the infinite number of unstable periodic orbits embedded in the chaotic invariant set provides sufficient information for estimating the generating partition. Here we present a general, dimension-independent, and efficient approach for this task based on optimizing a set of proximity functions defined with respect to periodic orbits. Our algorithm allows us to obtain the approximate location of the generating partition for the Ikeda-Hammel-Jones-Moloney map.

KW - symbolic dynamics

KW - strange attractor

KW - ring cavity

KW - henon map

U2 - 10.1103/PhysRevE.61.1353

DO - 10.1103/PhysRevE.61.1353

M3 - Article

VL - 61

SP - 1353

EP - 1356

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 - 2

ER -