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How does the Smaller Alignment Index (SALI) distinguish order from chaos? | | Ch. Skokos
; Ch. Antonopoulos
; T. C. Bountis
; M. N. Vrahatis
; | | Date: |
27 Dec 2002 | | Subject: | Chaotic Dynamics | nlin.CD | | Abstract: | The ability of the Smaller Alignment Index (SALI) to distinguish chaotic from ordered motion, has been demonstrated recently in several publications.cite{Sk01,GRACM} 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 {f 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. | | Source: | arXiv, nlin.CD/0301035 | | Services: | Forum | Review | PDF | Favorites | |
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