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 |
Fingerprint
Keywords
- Chaotic Attractor
- Homoclinic Orbit
- Lyapunov Exponent
- Stable Manifold
- Unstable Manifold
ASJC Scopus subject areas
- Applied Mathematics
Cite this
Introduction to Transient Chaos. / Lai, Ying-Cheng; Tél, Tamás.
Applied Mathematical Sciences (Switzerland). Springer, 2011. p. 3-35 (Applied Mathematical Sciences (Switzerland); Vol. 173).Research output: Chapter in Book/Report/Conference proceeding › Chapter
}
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 -