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- W2089364023 abstract "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 ${C}_{ensuremath{rho}}$ one of its generally many critical values at which the motion undergoes a stability-instability transition, the behavior of the largest Lyapunov exponent ensuremath{mu} as C approaches ${C}_{ensuremath{rho}}$ from the unstable region is given by ensuremath{mu}=constifmmodetimeselsetexttimesfi{}ensuremath{Vert}C-${C}_{ensuremath{rho}}$${ensuremath{Vert}}^{ensuremath{beta}}$, where ensuremath{beta}=(1/2), independent of the transition point, type of transitions, or the dimensionality of the system. We present numerical results for a three-dimensional Hamiltonian system which exhibits three types of stability-instability transitions, and for a two-dimensional Hamiltonian system which exhibits two types of transitions." @default.
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- W2089364023 date "1987-01-01" @default.
- W2089364023 modified "2023-09-30" @default.
- W2089364023 title "Stability-instability transitions in Hamiltonian systems ofndimensions" @default.
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- W2089364023 doi "https://doi.org/10.1103/physreva.35.847" @default.
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