Bifurcations of a Class of Nongeneric Quadratic Hamiltonian Systems under Quadratic Perturbations

2020 ◽  
pp. 149-156
Author(s):  
Li Baoyi ◽  
Xiao Dongmei ◽  
Zhang Zhifen
Keyword(s):  
Hamiltonian Systems ◽  
Quadratic Hamiltonian

On asymptotically quadratic Hamiltonian systems

1983 ◽  
Vol 7 (8) ◽  
pp. 929-931 ◽  
Author(s):  
V. Benci ◽  
A. Capozzi ◽  
D. Fortunato
Keyword(s):  
Hamiltonian Systems ◽  
Quadratic Hamiltonian

The Cyclicity of Period Annulus of Degenerate Quadratic Hamiltonian Systems with Polycycles S(2) or S(3) Under Perturbations of Piecewise Smooth Polynomials

2020 ◽  
Vol 30 (15) ◽  
pp. 2050230
Author(s):  
Jiaxin Wang ◽  
Liqin Zhao
Keyword(s):  
Hamiltonian Systems ◽  
Limit Cycles ◽  
Upper Bounds ◽  
Melnikov Function ◽  
Piecewise Smooth ◽  
Bifurcation Of Limit Cycles ◽  
First Order ◽  
Period Annulus ◽  
Quadratic Hamiltonian

In this paper, by using Picard–Fuchs equations and Chebyshev criterion, we study the bifurcation of limit cycles for degenerate quadratic Hamilton systems with polycycles [Formula: see text] or [Formula: see text] under the perturbations of piecewise smooth polynomials with degree [Formula: see text]. Roughly speaking, for [Formula: see text], a polycycle [Formula: see text] is cyclically ordered collection of [Formula: see text] saddles together with orbits connecting them in specified order. The discontinuity is on the line [Formula: see text]. If the first order Melnikov function is not equal to zero identically, it is proved that the upper bounds of the number of limit cycles bifurcating from each of the period annuli with the boundary [Formula: see text] and [Formula: see text] are respectively [Formula: see text] and [Formula: see text] (taking into account the multiplicity).

Even homoclinic orbits for super quadratic Hamiltonian systems

2010 ◽  
Vol 33 (14) ◽  
pp. 1755-1761 ◽  
Author(s):  
Jian Ding ◽  
Junxiang Xu ◽  
Fubao Zhang
Keyword(s):  
Hamiltonian Systems ◽  
Homoclinic Orbits ◽  
Quadratic Hamiltonian
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