### Abstract

We consider dynamical systems which possess two low-dimensional symmetric invariant subspaces. In each subspace, there is a chaotic attractor, and there are no other attractors in the phase space. As a parameter of the system changes, the largest Lyapunov exponents transverse to the invariant subspaces can change from negative to positive: the former corresponds to the situation where the basins of the attractors are intermingled, while the latter corresponds to the case where the system exhibits a two-state on-off intermittency. The phenomenon is investigated using a physical example where particles move in a two-dimensional potential, subjected to friction and periodic forcing.

Original language | English |
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Pages (from-to) | R3313-R3316 |

Number of pages | 4 |

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

Volume | 52 |

Issue number | 4 |

Publication status | Published - Oct 1995 |

### Keywords

- dynamic-systems
- oscillator
- chaos
- attractors
- motion