Stability-instability transitions in Hamiltonian systems ofndimensions

F. T. Hioe, Z. Deng
1987 Physical review. A, General physics  
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-C p | β where β= 1/2, independent of the transition point, type of transitions, or the dimensionality of the system.
more » ... lity 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. Disciplines Physics Comments 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 p, =const)&~C -C~~~, where P= 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.
doi:10.1103/physreva.35.847 pmid:9898211 fatcat:tghekkqm4ngnnpynbzmeb6s3ki