### Abstract

Computer simulations of partial differential equations of mathematical physics typically lead to some kind of high-dimensional dynamical system. When there is chaotic behavior we are faced with fundamental dynamical difficulties. We choose as a paradigm of such high-dimensional system a kicked double rotor. This system is investigated for parameter values at which it is strongly non-hyperbolic through a mechanism called unstable dimension variability, through which there are periodic orbits embedded in a chaotic attractor with different numbers of unstable directions. Our numerical investigation is primarily based on the analysis of the finite-time Lyapunov exponents, which gives us useful hints about the onset and evolution of unstable dimension variability for the double rotor map, as a system parameter (the forcing amplitude) is varied.

Original language | English |
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Pages (from-to) | 139-147 |

Number of pages | 8 |

Journal | Brazilian Journal of Physics |

Volume | 35 |

Publication status | Published - 2005 |

### Keywords

- UNSTABLE DIMENSION VARIABILITY
- LYAPUNOV EXPONENTS
- DYNAMIC-SYSTEMS
- SYNCHRONIZATION
- TRAJECTORIES

### Cite this

*Brazilian Journal of Physics*,

*35*, 139-147.