### Abstract

The Rikitake system as nonlinear dynamical systems in geomagnetism can be studied based on the KCC-theory and the unified field theory. Especially, the behavior of the magnetic field of the Rikitake system is represented in the electrical system projected from the electro-mechanical unified system. Then, the KCC-invariants for the electrical and mechanical systems can be obtained. The third invariant as the torsion tensor expresses the aperiodic behavior of the magnetic field. Moreover, as a result of the projection, a protrusion between the mechanical and electrical systems is represented by the Euler-Schouten tensor. This Euler-Schouten tensor and the third invariant consist of the same mutual-inductance. Therefore, the aperiodic behavior of the magnetic field can be characterized by the protrusion between the electrical and mechanical systems.

Original language | English |
---|---|

Journal | Nonlinear Analysis, Theory, Methods and Applications |

Volume | 71 |

Issue number | 12 |

DOIs | |

Publication status | Published - 2009 Dec 15 |

### Keywords

- Contact tensor calculus
- Euler-Schouten tensor
- KCC-theory
- Nonlinear dynamical systems
- Rikitake system
- Unified field theory

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics