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Volumn 143, Issue 3, 2001, Pages 449-497

The infinitesimal 16th Hilbert problem in the quadratic case

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EID: 0035580227     PISSN: 00209910     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002220000112     Document Type: Article
Times cited : (110)

References (42)
  • 1
    • 0002943096 scopus 로고
    • Le groupe de monodromie du déploiment des singularités isolées de courbes planes I
    • N. A'Campo, Le groupe de monodromie du déploiment des singularités isolées de courbes planes I, Math. Ann. 213 (1975) 1-32
    • (1975) Math. Ann. , vol.213 , pp. 1-32
    • A'Campo, N.1
  • 3
    • 0003318105 scopus 로고
    • Ordinary Differential Equations
    • Dynamical Systems I, Springer, Berlin
    • V.I. Arnold, Yu.S. Il'yashenko, Ordinary Differential Equations, in Dynamical Systems I, Enciclopaedia of Math. Sci., vol.1, Springer, Berlin, 1988
    • (1988) Enciclopaedia of Math. Sci. , vol.1
    • Arnold, V.I.1    Il'yashenko, Yu.S.2
  • 5
    • 84956129949 scopus 로고
    • Some unsolved problems in the theory of differential equations and mathematical physics
    • V.I. Arnold, Some unsolved problems in the theory of differential equations and mathematical physics, Russian Math. Surveys 44 (1989), no. 4, 157-171
    • (1989) Russian Math. Surveys , vol.44 , Issue.4 , pp. 157-171
    • Arnold, V.I.1
  • 6
    • 0001799499 scopus 로고
    • Ten problems in Theory of singularities and its applications
    • Amer. Math. Soc., Providence, RI
    • V.I. Arnold, Ten problems in Theory of singularities and its applications, 1-8, Adv. Soviet Math., 1, Amer. Math. Soc., Providence, RI, 1990
    • (1990) Adv. Soviet Math. , vol.1 , pp. 1-8
    • Arnold, V.I.1
  • 7
    • 0001520664 scopus 로고
    • A survey of quadratic systems
    • W.A. Coppel, A survey of quadratic systems. J. Differential Equations 2 (1966) 293-304
    • (1966) J. Differential Equations , vol.2 , pp. 293-304
    • Coppel, W.A.1
  • 8
    • 0003015617 scopus 로고
    • Sur les cycles limites
    • H. Dulac, Sur les cycles limites, Bull. Soc. Math. France, 51 (1923) 45-188
    • (1923) Bull. Soc. Math. France , vol.51 , pp. 45-188
    • Dulac, H.1
  • 10
    • 0030546995 scopus 로고    scopus 로고
    • Successive derivatives of a first return map, application to the study of a quadratic vector field
    • J.P. Françoise, Successive derivatives of a first return map, application to the study of a quadratic vector field, Erg. Theory and Dyn. Systems 16 (1996) 87-96
    • (1996) Erg. Theory and Dyn. Systems , vol.16 , pp. 87-96
    • Françoise, J.P.1
  • 12
    • 0001763980 scopus 로고
    • Limit cycles of perturbations of quadratic vector fields
    • L. Gavrilov, E. Horozov, Limit cycles of perturbations of quadratic vector fields, J. Math. Pures Appl. 72 (1993) 213-238
    • (1993) J. Math. Pures Appl. , vol.72 , pp. 213-238
    • Gavrilov, L.1    Horozov, E.2
  • 13
    • 0000445879 scopus 로고    scopus 로고
    • Isochronicity of plane polynomial Hamiltonian systems
    • L. Gavrilov, Isochronicity of plane polynomial Hamiltonian systems, Nonlinearity 10 (1997) 433-448
    • (1997) Nonlinearity , vol.10 , pp. 433-448
    • Gavrilov, L.1
  • 14
    • 0032324554 scopus 로고    scopus 로고
    • Petrov modules and zeros of Abelian integrals
    • L. Gavrilov, Petrov modules and zeros of Abelian integrals, Bull. Sci. math. 122 (1998) 571-584
    • (1998) Bull. Sci. Math. , vol.122 , pp. 571-584
    • Gavrilov, L.1
  • 15
    • 0033440641 scopus 로고    scopus 로고
    • Abelian integrals related to Morse polynomials and perturbation of plane Hamiltonian vector fields
    • L. Gavrilov, Abelian integrals related to Morse polynomials and perturbation of plane Hamiltonian vector fields, Ann. Inst. Fourier 49, 2 (1999) 611-652
    • (1999) Ann. Inst. Fourier , vol.49 , Issue.2 , pp. 611-652
    • Gavrilov, L.1
  • 16
    • 0034357798 scopus 로고    scopus 로고
    • Second order analysis in polynomially perturbed reversible quadratic Hamiltonian systems
    • to appear
    • L. Gavrilov, I.D. Iliev, Second order analysis in polynomially perturbed reversible quadratic Hamiltonian systems, Erg. Theory and Dyn. Systems, to appear in 2000
    • (2000) Erg. Theory and Dyn. Systems
    • Gavrilov, L.1    Iliev, I.D.2
  • 18
    • 0003059580 scopus 로고
    • Mathematical problems. Lecture delivered before the International Congress of Mathematicians at Paris in 1900
    • D. Hilbert, Mathematical problems. Lecture delivered before the International Congress of Mathematicians at Paris in 1900. Proc. Symp. Pure Math. 28 (1976) 1-34
    • (1976) Proc. Symp. Pure Math. , vol.28 , pp. 1-34
    • Hilbert, D.1
  • 19
    • 84963044168 scopus 로고
    • On the number of limit cycles in perturbations of quadratic Hamiltonian systems
    • E. Horozov, I.D. Iliev, On the number of limit cycles in perturbations of quadratic Hamiltonian systems, Proc. London Math. Soc. 69 (1994) 198-224
    • (1994) Proc. London Math. Soc. , vol.69 , pp. 198-224
    • Horozov, E.1    Iliev, I.D.2
  • 20
    • 0038884337 scopus 로고
    • On saddle-loop bifurcations of limit cycles in perturbations of quadratic Hamiltonian systems
    • E. Horozov, I.D. Iliev, On saddle-loop bifurcations of limit cycles in perturbations of quadratic Hamiltonian systems, J. Diff. Eqns. 113 (1994) 84-105
    • (1994) J. Diff. Eqns. , vol.113 , pp. 84-105
    • Horozov, E.1    Iliev, I.D.2
  • 21
    • 4344559894 scopus 로고
    • Hilbert-Arnold problem for cubic Hamiltonians and limit cycles
    • VSP Intern. Sci. Publ. Utrecht
    • E. Horozov, I.D. Iliev, Hilbert-Arnold problem for cubic Hamiltonians and limit cycles, in: Proc. Fourth Intern. Coll. Diff. Equations, VSP Intern. Sci. Publ. Utrecht (1994) 115-124
    • (1994) Proc. Fourth Intern. Coll. Diff. Equations , pp. 115-124
    • Horozov, E.1    Iliev, I.D.2
  • 22
    • 0030365273 scopus 로고    scopus 로고
    • Perturbations of quadratic Hamiltonian systems with symmetry
    • E. Horozov, I. Iliev, Perturbations of quadratic Hamiltonian systems with symmetry, Ann. Inst. Henri Poincaré 13 (1996) 17-56
    • (1996) Ann. Inst. Henri Poincaré , vol.13 , pp. 17-56
    • Horozov, E.1    Iliev, I.2
  • 23
    • 34250395888 scopus 로고
    • Dynkin digrams of singularities of functions of two variables
    • S.M. Husein-Zade, Dynkin digrams of singularities of functions of two variables, Functional Anal. Appl. 8 (1974) 10-13, 295-300
    • (1974) Functional Anal. Appl. , vol.8 , pp. 10-13
    • Husein-Zade, S.M.1
  • 24
    • 0032020006 scopus 로고    scopus 로고
    • Perturbations of quadratic centers
    • I.D. Iliev, Perturbations of quadratic centers, Bull. Sci. math. 22 (1998) 107-161
    • (1998) Bull. Sci. Math. , vol.22 , pp. 107-161
    • Iliev, I.D.1
  • 25
    • 0003137912 scopus 로고
    • w where R(z, w) is a polynomial
    • in russian
    • w where R(z, w) is a polynomial, USSR Math. Sbornik 78 (1969) 360-373 (in russian)
    • (1969) USSR Math. Sbornik , vol.78 , pp. 360-373
    • Il'yashenko, Yu.1
  • 26
    • 0010960789 scopus 로고
    • Dulac's memoir "On Limit Cycles" and related problems of the local theory of differential equations
    • Yu. Il'yashenko, Dulac's memoir "On Limit Cycles" and related problems of the local theory of differential equations, Russian Math. Surveys 40 (1985) 1-49
    • (1985) Russian Math. Surveys , vol.40 , pp. 1-49
    • Il'yashenko, Yu.1
  • 27
    • 0008872329 scopus 로고
    • Double exponential estimate for the number of zeros of complete Abelian integrals
    • Yu. Il'yashenko, S. Yakovenko, Double exponential estimate for the number of zeros of complete Abelian integrals, Invent, math. 121 (1995) 613-650
    • (1995) Invent, Math. , vol.121 , pp. 613-650
    • Il'yashenko, Yu.1    Yakovenko, S.2
  • 28
    • 0003278590 scopus 로고
    • Finitness theorems for limit cycles
    • AMS, Providence, RI
    • Yu. Il'yashenko, Finitness theorems for limit cycles, Transl. Math. Monographs 94, AMS, Providence, RI, 1991
    • (1991) Transl. Math. Monographs , vol.94
    • Il'yashenko, Yu.1
  • 29
    • 34250133017 scopus 로고
    • Real analytic manifolds with the property of finiteness, and complex abelian integrals
    • A.G. Khovanskiǐ, Real analytic manifolds with the property of finiteness, and complex abelian integrals. Functional Anal. Appl. 18 (1984) no. 2, 119-127
    • (1984) Functional Anal. Appl. , vol.18 , Issue.2 , pp. 119-127
    • Khovanskiǐ, A.G.1
  • 30
    • 0001888119 scopus 로고
    • Elliptic integrals and their nonoscillation
    • G.S. Petrov, Elliptic integrals and their nonoscillation, Funct. Anal. Appl. 20 (1986) 37-40
    • (1986) Funct. Anal. Appl. , vol.20 , pp. 37-40
    • Petrov, G.S.1
  • 31
    • 0000663138 scopus 로고
    • Mémoire sur les courbes définies par une équation différentielle
    • 3e série
    • H. Poincaré, Mémoire sur les courbes définies par une équation différentielle, J. de Mathématiques, 3e série 7 (1881) 375-422, 8 (1882) 251-296
    • (1881) J. de Mathématiques , vol.7 , pp. 375-422
    • Poincaré, H.1
  • 32
    • 0007220843 scopus 로고
    • H. Poincaré, Mémoire sur les courbes définies par une équation différentielle, J. de Mathématiques, 3e série 7 (1881) 375-422, 8 (1882) 251-296
    • (1882) J. de Mathématiques , vol.8 , pp. 251-296
  • 33
    • 0001277779 scopus 로고
    • Sur les courbes définies par les équations différentielles
    • 4e série
    • H. Poincaré, Sur les courbes définies par les équations différentielles, J. de Mathématiques, 4e série 1 (1885) 167-244
    • (1885) J. de Mathématiques , vol.1 , pp. 167-244
    • Poincaré, H.1
  • 34
    • 0001747859 scopus 로고
    • On dynamic systems close to Hamiltonian systems
    • in russian
    • L.S. Pontryagin, On dynamic systems close to Hamiltonian systems, Zh. Eksp. Teor. Fiz. 4 (1934) 234-238, in russian
    • (1934) Zh. Eksp. Teor. Fiz. , vol.4 , pp. 234-238
    • Pontryagin, L.S.1
  • 35
    • 51249171477 scopus 로고
    • On the number of limit cycles which appear by perturbation of separatrix loop of planar vector fields
    • R. Roussarie, On the number of limit cycles which appear by perturbation of separatrix loop of planar vector fields, Bol. Soc. Bras. Math. (2), 17 (1986) 67-101
    • (1986) Bol. Soc. Bras. Math. (2) , vol.17 , pp. 67-101
    • Roussarie, R.1
  • 36
    • 0003244212 scopus 로고    scopus 로고
    • Bifurcations of Planar Vector Fields and Hubert's sixteenth Problem
    • Birkhauser
    • R. Roussarie, Bifurcations of Planar Vector Fields and Hubert's sixteenth Problem, Progress in Mathematics vol. 164, Birkhauser, 1998
    • (1998) Progress in Mathematics , vol.164
    • Roussarie, R.1
  • 37
    • 36149036159 scopus 로고
    • Cyclicité fini des lacets et des points cuspidaux
    • R. Roussarie, Cyclicité fini des lacets et des points cuspidaux, Nonlinearity 2 (1988) 73-117
    • (1988) Nonlinearity , vol.2 , pp. 73-117
    • Roussarie, R.1
  • 40
    • 0002232057 scopus 로고
    • Estimate of the number of zeros of Abelian integrals depending on a parameters and limit cycles
    • A.N. Varchenko, Estimate of the number of zeros of Abelian integrals depending on a parameters and limit cycles, Funct. Analysis and Appl. 18 (1984) 98-108
    • (1984) Funct. Analysis and Appl. , vol.18 , pp. 98-108
    • Varchenko, A.N.1
  • 41
    • 0033585197 scopus 로고    scopus 로고
    • The distribution of limit cycles in quadratic systems with four finite singularities
    • A. Zegeling, R.E. Kooij, The distribution of limit cycles in quadratic systems with four finite singularities, J. Diff. Equations 151 (1999) 373-385
    • (1999) J. Diff. Equations , vol.151 , pp. 373-385
    • Zegeling, A.1    Kooij, R.E.2
  • 42
    • 0000813963 scopus 로고
    • Quadratic systems with center and their perturbations
    • H. Żoładek, Quadratic systems with center and their perturbations, J. Diff. Equations 109 (1994) 223-273
    • (1994) J. Diff. Equations , vol.109 , pp. 223-273
    • Zoładek, H.1


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