Perturbations of symmetric elliptic Hamiltonians of degree four in a complex domain
作者： Bassem Ben Hamed , Ameni Gargouri , Lubomir Gavrilov
DOI: 10.1016/J.JMAA.2014.11.018
关键词: Mathematics 、 Domain (mathematical analysis) 、 Bifurcation diagram 、 Mathematical analysis 、 Duffing equation 、 Melnikov method 、 Annulus (mathematics) 、 Degree (graph theory)
摘要: … eight-loop or … elliptic integrals of first and second kind I 0 , I 2 , I 4 ′ (4) M k ( h ) = λ 0 k I 0 ( h ) + λ 2 k I 2 ( h ) + λ 4 k I 4 ′ ( h ) . We recall that if P ε is the first return map of the perturbed …
elsevier.com
sci-hub.se 参考文章(13)
Robert H. Roussarie, Bifurcations of Planar Vector Fields and Hilbert's Sixteenth Problem ,(1998)
Lubomir Gavrilov, Petrov modules and zeros of Abelian integrals Bulletin Des Sciences Mathematiques. ,vol. 122, pp. 571- 584 ,(1998) , 10.1016/S0007-4497(99)80004-9
Lubomir Gavrilov, On the number of limit cycles which appear by perturbation of Hamiltonian two-saddle cycles of planar vector fields Bulletin of The Brazilian Mathematical Society. ,vol. 42, pp. 1- 23 ,(2011) , 10.1007/S00574-011-0001-Z
I.D. Iliev, L.M. Perko, Higher Order Bifurcations of Limit Cycles Journal of Differential Equations. ,vol. 154, pp. 339- 363 ,(1999) , 10.1006/JDEQ.1998.3549
G. S. Petrov, Complex zeros of an elliptic integral Functional Analysis and Its Applications. ,vol. 23, pp. 160- 161 ,(1987) , 10.1007/BF01078797
Lubomir Gavrilov, The infinitesimal 16th Hilbert problem in the quadratic case Inventiones Mathematicae. ,vol. 143, pp. 449- 497 ,(2001) , 10.1007/PL00005798
Chengzhi Li, Pavao Mardešić, Robert Roussarie, Perturbations of symmetric elliptic Hamiltonians of degree four Journal of Differential Equations. ,vol. 231, pp. 78- 91 ,(2006) , 10.1016/J.JDE.2006.07.016
Changjian Liu, Estimate of the number of zeros of Abelian integrals for an elliptic Hamiltonian with figure-of-eight loop Nonlinearity. ,vol. 16, pp. 1151- 1163 ,(2003) , 10.1088/0951-7715/16/3/319
J.M. Jebrane, H. Zoladek, Abelian Integrals in Non-symmetric Perturbation of Symmetric Hamiltonian Vector Field Advances in Applied Mathematics. ,vol. 15, pp. 1- 12 ,(1994) , 10.1006/AAMA.1994.1001
Freddy Dumortier, Chengzhi Li, Perturbation from an elliptic Hamiltonian of degree four—IV figure eight-loop Journal of Differential Equations. ,vol. 188, pp. 512- 554 ,(2003) , 10.1016/S0022-0396(02)00111-0