### Abstract

Statistics of shadowing time in nonhyperbolic chaotic systems is discussed with unstable dimension variability. No true trajectory of reasonable length can be found to exist near any numerically generated trajectory, when the dimension of the unstable eigenspace changes along a trajectory in the invariant set. It is found that an important quantity characterizing the shadowability of numerical trajectories is the shadowing time. It measures for how long a trajectory remains valid.

Original language | English (US) |
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Article number | 016213 |

Pages (from-to) | 162131-1621310 |

Number of pages | 1459180 |

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

Volume | 69 |

Issue number | 1 2 |

State | Published - Jan 1 2004 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics

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## Cite this

Do, Y., & Lai, Y-C. (2004). Statistics of shadowing time in nonhyperbolic chaotic systems with unstable dimension variability.

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*,*69*(1 2), 162131-1621310. [016213].