کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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6416991 | 1338504 | 2016 | 26 صفحه PDF | دانلود رایگان |
In this paper we study the global dynamics of the Hamiltonian systems xË=Hy(x,y), yË=âHx(x,y), where the Hamiltonian function H has the particular form H(x,y)=y2/2+P(x)/Q(x), P(x),Q(x)âR[x] are polynomials, in particular H is the sum of the kinetic and a rational potential energies. Firstly, we provide the normal forms by a suitable μ-symplectic change of variables. Then, the global topological classification of the phase portraits of these systems having canonical forms in the Poincaré disk in the cases where degree(P)=0,1,2 and degree(Q)=0,1,2 are studied as a function of the parameters that define each polynomial. We use a blow-up technique for finite equilibrium points and the Poincaré compactification for the infinite equilibrium points. Finally, we show some applications.
Journal: Journal of Differential Equations - Volume 261, Issue 11, 5 December 2016, Pages 5923-5948