Detecting order and chaos in Hamiltonian systems by the SALI method

By Charalampos Skokos, Chris G. Antonopoulos, T. Bountis, Michael N. Vrahatis. 2004

187 citations recorded by the source corpus.

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 ,σ 2 i.e. SALI ∝ e −(σ

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/67a250a8777e925da79a97946734d2c476141418

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. Georg A. Gottwald
2. Ian Melbourne
3. Charalampos Skokos

In Statistical and Nonlinear Physics

1. Charalampos Skokos
2. Georg A. Gottwald
3. Ian Melbourne
4. Alexander I. Bufetov
5. E. Rio

Citations in the corpus

• The Lyapunov Characteristic Exponents and Their Computation (2008, methodology): “Actually GALI2 ∝ SALI.”
• On the Implementation of the 0-1 Test for Chaos (2009, methodology): “The test has been applied to noisy numerical data [9], experimental data [5], quasiperiodically forced systems and strange nonchaotic attractors [3], Hamiltonian systems [26], nonsmooth systems [15] and fluid dynamics [18].”