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The Smaller Alignment Index (SALI) is a very useful and efficient indicatorthat can distinguish rapidly and with certainty between ordered and chaoticmotion in Hamiltonian systems. This is based on the different behavior of theSALI in the two cases, as it fluctuates around non-zero values for orderedorbits and converges exponentially to zero for chaotic orbits. In this paper wepresent a detailed numerical study, comparing the advantages of the SALI tothose of the Maximal Lyapunov Exponent (MLE), which is the traditionalindicator of chaos detection in dynamical systems. Exploiting these advantages,we demonstrate how the SALI can be used to identify even tiny regions of orderand chaos in Hamiltonian systems of 2 and 3 degrees of freedom.

SALI: An Efficient Indicator of Chaos with Application to 2 and 3 Degrees of Freedom Hamiltonian Systems