### 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 (US) |
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Title of host publication | Applied Mathematical Sciences (Switzerland) |

Publisher | Springer |

Pages | 3-35 |

Number of pages | 33 |

DOIs | |

State | Published - Jan 1 2011 |

### Publication series

Name | Applied Mathematical Sciences (Switzerland) |
---|---|

Volume | 173 |

ISSN (Print) | 0066-5452 |

ISSN (Electronic) | 2196-968X |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Applied Mathematics

### Cite this

*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

**Introduction to Transient Chaos.** / Lai, Ying-Cheng; Tél, Tamás.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

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

}

TY - CHAP

T1 - Introduction to Transient Chaos

AU - Lai, Ying-Cheng

AU - Tél, Tamás

PY - 2011/1/1

Y1 - 2011/1/1

N2 - 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.

AB - 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.

KW - Chaotic Attractor

KW - Homoclinic Orbit

KW - Lyapunov Exponent

KW - Stable Manifold

KW - Unstable Manifold

UR - http://www.scopus.com/inward/record.url?scp=85067993334&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85067993334&partnerID=8YFLogxK

U2 - 10.1007/978-1-4419-6987-3_1

DO - 10.1007/978-1-4419-6987-3_1

M3 - Chapter

AN - SCOPUS:85067993334

T3 - Applied Mathematical Sciences (Switzerland)

SP - 3

EP - 35

BT - Applied Mathematical Sciences (Switzerland)

PB - Springer

ER -