Abstract
We use the smaller alignment index (SALI) to distinguish rapidly and with certainty between ordered and chaotic motion in Hamiltonian flows. This distinction is based on the different behaviour of the SALI for the two cases: the index fluctuates around non-zero values for ordered orbits, while it tends rapidly to zero for chaotic orbits. We present a detailed study of SALI's behaviour for chaotic orbits and show that in this case the SALI exponentially converges to zero, following a time rate depending on the difference of the two largest Lyapunov exponents σ1, σ2 i.e. SALI ∝ e-(σ1-σ2)t. Exploiting the advantages of the SALI method, we demonstrate how one can rapidly identify even tiny regions of order or chaos in the phase space of Hamiltonian systems of two and three degrees of freedom.
| Original language | English |
|---|---|
| Pages (from-to) | 6269-6284 |
| Number of pages | 16 |
| Journal | Journal of Physics A: Mathematical and General |
| Volume | 37 |
| Issue number | 24 |
| DOIs | |
| Publication status | Published - Jun 18 2004 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematical Physics
Cite this
Detecting order and chaos in Hamiltonian systems by the SALI method. / Skokos, Ch; Antonopoulos, Ch; Bountis, T. C.; Vrahatis, M. N.
In: Journal of Physics A: Mathematical and General, Vol. 37, No. 24, 18.06.2004, p. 6269-6284.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Detecting order and chaos in Hamiltonian systems by the SALI method
AU - Skokos, Ch
AU - Antonopoulos, Ch
AU - Bountis, T. C.
AU - Vrahatis, M. N.
PY - 2004/6/18
Y1 - 2004/6/18
N2 - We use the smaller alignment index (SALI) to distinguish rapidly and with certainty between ordered and chaotic motion in Hamiltonian flows. This distinction is based on the different behaviour of the SALI for the two cases: the index fluctuates around non-zero values for ordered orbits, while it tends rapidly to zero for chaotic orbits. We present a detailed study of SALI's behaviour for chaotic orbits and show that in this case the SALI exponentially converges to zero, following a time rate depending on the difference of the two largest Lyapunov exponents σ1, σ2 i.e. SALI ∝ e-(σ1-σ2)t. Exploiting the advantages of the SALI method, we demonstrate how one can rapidly identify even tiny regions of order or chaos in the phase space of Hamiltonian systems of two and three degrees of freedom.
AB - We use the smaller alignment index (SALI) to distinguish rapidly and with certainty between ordered and chaotic motion in Hamiltonian flows. This distinction is based on the different behaviour of the SALI for the two cases: the index fluctuates around non-zero values for ordered orbits, while it tends rapidly to zero for chaotic orbits. We present a detailed study of SALI's behaviour for chaotic orbits and show that in this case the SALI exponentially converges to zero, following a time rate depending on the difference of the two largest Lyapunov exponents σ1, σ2 i.e. SALI ∝ e-(σ1-σ2)t. Exploiting the advantages of the SALI method, we demonstrate how one can rapidly identify even tiny regions of order or chaos in the phase space of Hamiltonian systems of two and three degrees of freedom.
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UR - http://www.scopus.com/inward/citedby.url?scp=3042620995&partnerID=8YFLogxK
U2 - 10.1088/0305-4470/37/24/006
DO - 10.1088/0305-4470/37/24/006
M3 - Article
VL - 37
SP - 6269
EP - 6284
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
SN - 1751-8113
IS - 24
ER -