### Abstract

The experimental detection of unstable periodic orbits in dynamical systems, especially those which yield short, noisy or nonstationary data sets, is a current topic of interest in many research areas. Unfortunately, for such data sets, only a few of the lowest order periods can be detected with quantifiable statistical accuracy. The primary observable is the number of encounters the general trajectory has with a particular orbit. Here we show that, in the limit of large period, this quantity scales exponentially with the period, and that this scaling is robust to dynamical noise. (C) 1998 American Institute of Physics. [S1054-1500(98)00904-5].

Original language | English |
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Pages (from-to) | 853-860 |

Number of pages | 8 |

Journal | Chaos |

Volume | 8 |

Issue number | 4 |

DOIs | |

Publication status | Published - Dec 1998 |

### Keywords

- low-dimensional dynamics
- time-series
- strange sets
- topological analysis
- plateau onset
- attractors
- biology
- occur
- laws

## Cite this

*Chaos*,

*8*(4), 853-860. https://doi.org/10.1063/1.166371