### Abstract

We examine the interplay between complexity and unstable periodic orbits in high-dimensional chaotic systems. Argument and numerical evidence are presented suggesting that complexity can arise when the system is severely nonhyperbolic in the sense that periodic orbits with a distinct number of unstable directions coexist and are densely mixed. A quantitative measure is introduced to characterize this unstable dimension variability.

Original language | English |
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Pages (from-to) | R3807-R3810 |

Number of pages | 4 |

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

Volume | 59 |

Issue number | 4 |

Publication status | Published - Apr 1999 |

### Keywords

- PERIODIC-ORBITS
- DYNAMICAL-SYSTEMS
- RING CAVITY
- ATTRACTORS
- BASINS

## Cite this

Lai, Y. C., & Lai, Y-C. (1999). Unstable dimension variability and complexity in chaotic systems.

*Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*,*59*(4), R3807-R3810.