We show analytically that for a class of simple periodic motions in a general Hamiltonian system of n dimensions, if C is a parameter of the system and Cz one of its generally many critical values at which the motion undergoes a stability-instability transition, the behavior of the largest Lyapunov exponent p as C approaches Ce from the unstable region is given by µ, =constX |~ C—Cp |β where β= 1/2, independent of the transition point, type of transitions, or the dimensionality of the system. We present numerical results for a three-dimensional Harniltonian system which exhibits three types of stability-instability transitions, and for a two-dimensional Hamiltonian system which exhibits two types of transitions.
Hioe, Foek T. and Deng, Z (1987). "Stability-instability transitions in Hamiltonian systems of n dimensions." Physical Review A 35.2, 847-856.
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