### Abstract

We investigate how the transition to chaos with multiple positive Lyapunov exponents can be characterized by the set of infinite number of unstable periodic orbits embedded in the chaotic invariant set. We argue and provide numerical confirmation that the transition is generally accompanied by a nonhyperbolic behavior: unstable dimension variability. As a consequence, the Lyapunov exponents, except for the largest one, pass through zero continuously. (C) 2000 Elsevier Science B.V. All rights reserved.

Original language | English |
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Pages (from-to) | 308-313 |

Number of pages | 6 |

Journal | Physics Letters A |

Volume | 270 |

Issue number | 6 |

Publication status | Published - 12 Jun 2000 |

### Keywords

- HIGH-DIMENSIONAL CHAOS
- FRACTAL DIMENSION
- DYNAMICAL-SYSTEMS
- RING CAVITY
- ATTRACTORS
- VARIABILITY
- TURBULENCE
- CRISES
- SPACE

## Cite this

Davidchack, R., Lai, Y. C., & Lai, Y-C. (2000). Characterization of transition to chaos with multiple positive - Lyapunov exponents by unstable periodic orbits.

*Physics Letters A*,*270*(6), 308-313.