### 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 |
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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

Davidchack, R. L., Lai, Y-C., Bollt, E. M., & Dhamala, M. (2000). Estimating generating partitions of chaotic systems by unstable periodic orbits.

*Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*,*61*(2), 1353-1356. https://doi.org/10.1103/PhysRevE.61.1353