Abstract
The ability of the Smaller Alignment Index (SALI) to distinguish chaotic from ordered motion, has been demonstrated recently in several publications. [Ch. Skokos, J. of Phys. A 34 (2001), 10029. Ch. Skokos, Ch. Antonopoulos, T. C. Bountis and M. N. Vrahatis, in Proceedings of the 4th GRACM Congress on Computational Mechanics, ed. D. T. Tsahalis (Univ. Patras, Patras, 2002), Vol. IV, p. 1496; in Libration Point Orbits and Applications, ed. G. Gómez, M. W. Lo and J. J. Masdemont (World Scientific, 2003), in press, nlin.CD/0210053.] Basically it is observed that in chaotic regions the SALI goes to zero very rapidly, while it fluctuates around a nonzero value in ordered regions. In this paper, we make a first step forward explaining these results by studying in detail the evolution of small deviations from regular orbits lying on the invariant tori of an integrable 2D Hamiltonian system. We show that, in general, any two initial deviation vectors will eventually fall on the "tangent space" of the torus, pointing in different directions due to the different dynamics of the 2 integrals of motion, which means that the SALI (or the smaller angle between these vectors) will oscillate away from zero for all time.
| Original language | English |
|---|---|
| Pages (from-to) | 439-443 |
| Number of pages | 5 |
| Journal | Progress of Theoretical Physics Supplement |
| Volume | 150 |
| Publication status | Published - 2003 |
| Externally published | Yes |
Fingerprint
ASJC Scopus subject areas
- Physics and Astronomy(all)
Cite this
How Does the Smaller Alignment Index (SALI) Distinguish Order from Chaos? / Skokos, Charalampos; Antonopoulos, Chris; Bountis, Tassos C.; Vrahatis, Michael N.
In: Progress of Theoretical Physics Supplement, Vol. 150, 2003, p. 439-443.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - How Does the Smaller Alignment Index (SALI) Distinguish Order from Chaos?
AU - Skokos, Charalampos
AU - Antonopoulos, Chris
AU - Bountis, Tassos C.
AU - Vrahatis, Michael N.
PY - 2003
Y1 - 2003
N2 - The ability of the Smaller Alignment Index (SALI) to distinguish chaotic from ordered motion, has been demonstrated recently in several publications. [Ch. Skokos, J. of Phys. A 34 (2001), 10029. Ch. Skokos, Ch. Antonopoulos, T. C. Bountis and M. N. Vrahatis, in Proceedings of the 4th GRACM Congress on Computational Mechanics, ed. D. T. Tsahalis (Univ. Patras, Patras, 2002), Vol. IV, p. 1496; in Libration Point Orbits and Applications, ed. G. Gómez, M. W. Lo and J. J. Masdemont (World Scientific, 2003), in press, nlin.CD/0210053.] Basically it is observed that in chaotic regions the SALI goes to zero very rapidly, while it fluctuates around a nonzero value in ordered regions. In this paper, we make a first step forward explaining these results by studying in detail the evolution of small deviations from regular orbits lying on the invariant tori of an integrable 2D Hamiltonian system. We show that, in general, any two initial deviation vectors will eventually fall on the "tangent space" of the torus, pointing in different directions due to the different dynamics of the 2 integrals of motion, which means that the SALI (or the smaller angle between these vectors) will oscillate away from zero for all time.
AB - The ability of the Smaller Alignment Index (SALI) to distinguish chaotic from ordered motion, has been demonstrated recently in several publications. [Ch. Skokos, J. of Phys. A 34 (2001), 10029. Ch. Skokos, Ch. Antonopoulos, T. C. Bountis and M. N. Vrahatis, in Proceedings of the 4th GRACM Congress on Computational Mechanics, ed. D. T. Tsahalis (Univ. Patras, Patras, 2002), Vol. IV, p. 1496; in Libration Point Orbits and Applications, ed. G. Gómez, M. W. Lo and J. J. Masdemont (World Scientific, 2003), in press, nlin.CD/0210053.] Basically it is observed that in chaotic regions the SALI goes to zero very rapidly, while it fluctuates around a nonzero value in ordered regions. In this paper, we make a first step forward explaining these results by studying in detail the evolution of small deviations from regular orbits lying on the invariant tori of an integrable 2D Hamiltonian system. We show that, in general, any two initial deviation vectors will eventually fall on the "tangent space" of the torus, pointing in different directions due to the different dynamics of the 2 integrals of motion, which means that the SALI (or the smaller angle between these vectors) will oscillate away from zero for all time.
UR - http://www.scopus.com/inward/record.url?scp=0345411904&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0345411904&partnerID=8YFLogxK
M3 - Article
VL - 150
SP - 439
EP - 443
JO - Progress of Theoretical Physics Supplement
JF - Progress of Theoretical Physics Supplement
SN - 0375-9687
ER -