Abelian integrals related to Morse polynomials and perturbations of plane hamiltonian vector fields

© Annales de l’institut Fourier, 1999, tous droits réservés. L’accès aux archives de la revue « Annales de l’institut Fourier » (http://annalif.ujf-grenoble.fr/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.

[1]  Iliya D. Iliev,et al.  On the Number of Limit Cycles in Perturbations of Quadratic Hamiltonian Systems , 1994 .

[2]  G. S. Petrov,et al.  Number of zeros of complete elliptic integrals , 1984 .

[3]  J. Sotomayor,et al.  Abelian integrals in unfoldings of codimension 3 singular planar vector fields , 1991 .

[4]  Iliya D. Iliev,et al.  Higher-order Melnikov functions for degenerate cubic Hamiltonians , 1996, Advances in Differential Equations.

[5]  Isochronicity of plane polynomial Hamiltonian systems , 1997 .

[6]  Iliya D. Iliev,et al.  Perturbations of quadratic centers , 1998 .

[7]  Lubomir Gavrilov Nonoscillation of Elliptic Integrals Related to Cubic Polynomials with Symmetry of Order Three , 1998 .

[8]  Y. Ilyashenko,et al.  Dulac's memoir “On limit cycles” and related problems of the local theory of differential equations , 1985 .

[9]  G. S. Petrov Elliptic integrals and their nonoscillation , 1986 .

[10]  Lubomir Gavrilov,et al.  Petrov modules and zeros of Abelian integrals , 1998 .

[11]  H. Zoladek,et al.  Quadratic Systems with Center and Their Perturbations , 1994 .

[12]  P. Hartman Ordinary Differential Equations , 1965 .

[13]  N. A'campo Le groupe de monodromie du déploiement des singularités isolées de courbes planes I , 1975 .

[14]  Iliya D. Iliev,et al.  Linear estimate for the number of zeros of Abelian integrals with cubic Hamiltonians , 1998 .

[15]  G. S. Petrov,et al.  Non-oscillation of elliptic integrals , 1990 .

[16]  Vladimir Igorevich Arnold,et al.  Geometrical Methods in the Theory of Ordinary Differential Equations , 1983 .

[17]  Egbert Brieskorn,et al.  Die monodromie der isolierten singularitäten von hyperflächen , 1970 .

[18]  B. Malgrange Intégrales asymptotiques et monodromie , 1974 .

[19]  Robert Roussarie,et al.  On the number of limit cycles which appear by perturbation of separatrix loop of planar vector fields , 1986 .

[20]  P. Mardešić The number of limit cycles of polynomial deformations of a Hamiltonian vector field , 1990 .

[21]  Joe W. Harris,et al.  Principles of Algebraic Geometry , 1978 .

[22]  Marcos Sebastiani,et al.  Preuve d'une conjecture de Brieskorn , 1970 .

[23]  Christiane Rousseau,et al.  Zeroes of complete elliptic integrals for 1:2 resonance , 1991 .