### Abstract

In numerical or experimental investigations one never has infinitely long time intervals at one’s disposal. In fact, what is needed for the observation of chaos is a well-defined separation of time scales. Let t _{0} denote the internal characteristic time of the system. In continuous-time problems, t _{0} can be the average turnover time of trajectories on a Poincaré map in the phase space. In a driven system, it is the driving period. In discrete-time dynamics, t _{0} can be the time step itself.

Original language | English |
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Title of host publication | Applied Mathematical Sciences (Switzerland) |

Publisher | Springer |

Pages | 3-35 |

Number of pages | 33 |

DOIs | |

Publication status | Published - Jan 1 2011 |

### Publication series

Name | Applied Mathematical Sciences (Switzerland) |
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Volume | 173 |

ISSN (Print) | 0066-5452 |

ISSN (Electronic) | 2196-968X |

### Keywords

- Chaotic Attractor
- Homoclinic Orbit
- Lyapunov Exponent
- Stable Manifold
- Unstable Manifold

### ASJC Scopus subject areas

- Applied Mathematics

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## Cite this

Lai, Y. C., & Tél, T. (2011). Introduction to Transient Chaos. In

*Applied Mathematical Sciences (Switzerland)*(pp. 3-35). (Applied Mathematical Sciences (Switzerland); Vol. 173). Springer. https://doi.org/10.1007/978-1-4419-6987-3_1