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) |
|---|---|
| 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 |
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