Majorations affines du nombre de zéros d'intégrales abéliennes pour les hamiltoniens quartiques elliptiques

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1. [1] Gavrilov ( L.) .— Petrov modules and zeros of Abelian integrals, Bull. Sci. Math. (à paraître). Zbl0964.32022MR1668534
2. [2] Gavrilov ( L.) .— Nonoscillation of elliptic integrals related to cubic polynomials with symmetry of order three, Bull. Lond. Math. Soc. (à paraître) . Zbl0959.37039MR1608110
3. [3] Girard ( F.) .- Une propriété de Chebychev pour certaines intégrales abéliennes généralisées, C. R. Acad. Sci.Paris, 326, Série I (1998), pp. 471-476. Zbl0926.34019MR1648971
4. [4] Ha Huy Vui ET Nguyen Le Anh .— Le comportement géométrique à l'infini des polynômes de deux variables complexes, C. R. Acad. Sci.Paris, 309, Série I (1989), pp. 183-186. Zbl0685.32006MR1005635
5. [5] Horozov ( E.) et Iliev ( I.D.) .— Linear estimate for the number ofzeros of Abelian integrals with cubic Hamiltonians, Conférence à Luminy, octobre 1997. MR1660361
6. [6] Iliev ( D.) .— On second order bifurcations of limit cycles, J. Lond. Math. Soc.1998. Zbl0922.34037MR1668195
7. [7] Iliev ( D.) et Perko ( L.) .— Higher order bifurcation of limit cycles, (à paraître). Zbl0926.34033
8. [8] IL'YASHENKO ( Yu S.) . - The multiplicity of limit cycles arising from perturbation of the form w' = P2 /Q1 of a Hamilton equation in the real and complex domain, Amer. Math. Soc. Trans.118, n° 2 (1982). Zbl0494.34018
9. [9] IL'YASHENKO ( Yu S.) et Yakovenko ( S.), .- Double exponential estimate for the number of zeros of complete Abelian integrals, Invent. Math.121, n° 3 (1995), pp. 613-650. Zbl0865.34007MR1353310
10. [10] IL'YASHENKO ( Yu S.) et Yakovenko ( S.), .— Counting real zeros of analytic function satisying linear ordinary differential equations, J. Diff. Equ.126, n° 1 (1996), pp. 87-105. Zbl0847.34010MR1382058
11. [11] Jebrane ( M.) et Zoladek ( H.) .- Abelian integrals in non-symmetricperturbation of symmetric Hamiltonian vector field, Adv. Appl Math.15 (1994), pp. 1-12. Zbl0802.34041MR1260295
12. [12] Khovanski ( A.) .— Real analytic manifolds with finiteness properties and complex Abelian integrals, Funct. Anal. Appl.18 (1984), pp. 119-128. Zbl0584.32016
13. [13] Malgrange ( B.) .- Intégrales asymptotiques et monodromie, Ann. Scient. Ec. Norm. Supp.7 (1974), pp. 405-430. Zbl0305.32008MR372243
14. [14] Mardešiċ ( P.) .— The number of limit cycles of polynomial perturbations of a Hamiltonian vector field, Erg. Th. Dyn. Sys.10 (1990), pp. 523-529. Zbl0691.58031MR1074317
15. [15] Novikov ( D.) et Yakovenko ( S.) .— Simple exponential estimate for the number of real zeros of complete Abelian integrals, Ann. Inst. Fourier45 (1995), pp. 897-927. Zbl0832.58028MR1359833
16. [16] Petrov ( G.S.) .— Elliptic integrals and their non-oscillatorness, Funct. Anal. Appl.20, n° 1 (1986), pp. 46-49. Zbl0656.34017MR831048
17. [17] Petrov ( G.S.) .- Complex zeros of an elliptic integral, Funct. Anal. Appl.21 (1987), n° 3, pp. 87-88. Zbl0625.33001MR911784
18. [18] Petrov ( G.S.) . - Non-oscillatorness of elliptic integrals, Funct. Anal. Appl.24, n° 3 (1990), pp. 45-50. Zbl0738.33013
19. [19] Varchenko ( A.N.) .— Estimate of the number of zeros of Abelian integrals depending on parameters and limit cycles, Funct. Anal. Appl.18 (1984), pp. 98-108. Zbl0578.58035MR745696