메뉴 건너뛰기




Volumn 221, Issue 2, 2006, Pages 309-342

A unified proof on the weak Hilbert 16th problem for n = 2

Author keywords

Abelian integral; Centroid curve; Deformation argument; Weak Hilbert 16th problem

Indexed keywords


EID: 30944447320     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jde.2005.01.009     Document Type: Article
Times cited : (77)

References (26)
  • 1
    • 0000465791 scopus 로고
    • On the number of limit cycles which appear with the variation of the coefficients from an equilibrium position of focus or center type
    • N.N. Bautin On the number of limit cycles which appear with the variation of the coefficients from an equilibrium position of focus or center type Amer. Math. Soc. Translations 100 (1954) 1-19
    • (1954) Amer. Math. Soc. Translations , vol.100 , pp. 1-19
    • Bautin, N.N.1
  • 2
    • 84972541905 scopus 로고
    • The period function of a Hamiltonian quadratic system
    • W.A. Coppel L. Gavrilov The period function of a Hamiltonian quadratic system Differential Integral Equations 6 (1993) 1357-1365
    • (1993) Differential Integral Equations , vol.6 , pp. 1357-1365
    • Coppel, W.A.1    Gavrilov, L.2
  • 3
    • 0036012116 scopus 로고    scopus 로고
    • The cyclicity of period annulus of degenerate quadratic Hamiltonian system with elliptic segment loops
    • S.-N. Chow C. Li Y. Yi The cyclicity of period annulus of degenerate quadratic Hamiltonian system with elliptic segment loops Ergodic Theory Dyn. Systems 22 (2002) 349-374
    • (2002) Ergodic Theory Dyn. Systems , vol.22 , pp. 349-374
    • Chow, S.-N.1    Li, C.2    Yi, Y.3
  • 4
    • 0035841053 scopus 로고    scopus 로고
    • Perturbation from an elliptic Hamiltonian of degree four, I saddle loop and two saddle cycle
    • F. Dumortier C. Li Perturbation from an elliptic Hamiltonian of degree four, I saddle loop and two saddle cycle J. Differential Equations 176 (2001) 114-157
    • (2001) J. Differential Equations , vol.176 , pp. 114-157
    • Dumortier, F.1    Li, C.2
  • 5
    • 0035580227 scopus 로고    scopus 로고
    • The infinitesimal 16th Hilbert problem in the quadratic case
    • L. Gavrilov The infinitesimal 16th Hilbert problem in the quadratic case Invent. Math. 143 (2001) 449-497
    • (2001) Invent. Math. , vol.143 , pp. 449-497
    • Gavrilov, L.1
  • 6
    • 0034357798 scopus 로고    scopus 로고
    • Second order analysis in polynomially perturbed reversible quadratic Hamiltonian systems
    • L. Gavrilov I.D. Iliev Second order analysis in polynomially perturbed reversible quadratic Hamiltonian systems Ergodic Theory Dyn. Systems 20 (2000) 1671-1686
    • (2000) Ergodic Theory Dyn. Systems , vol.20 , pp. 1671-1686
    • Gavrilov, L.1    Iliev, I.D.2
  • 7
    • 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
  • 8
    • 0038884337 scopus 로고
    • On saddle-loop bifurcation of limit cycles in perturbations of quadratic Hamiltonian systems
    • E. Horozov I.D. Iliev On saddle-loop bifurcation of limit cycles in perturbations of quadratic Hamiltonian systems J. Differential Equations 113 (1994) 84-105
    • (1994) J. Differential Equations , vol.113 , pp. 84-105
    • Horozov, E.1    Iliev, I.D.2
  • 10
    • 0347466739 scopus 로고    scopus 로고
    • Linear estimate for the number of zeros of Abelian integrals with cubic Hamiltonian
    • E. Horozov I.D. Iliev Linear estimate for the number of zeros of Abelian integrals with cubic Hamiltonian Nonlinearity 11 (1998) 1521-1537
    • (1998) Nonlinearity , vol.11 , pp. 1521-1537
    • Horozov, E.1    Iliev, I.D.2
  • 11
    • 0001722685 scopus 로고    scopus 로고
    • High-order Melnikov functions for degenerate cubic Hamiltonian
    • I.D. Iliev High-order Melnikov functions for degenerate cubic Hamiltonian Adv. Differential Equations 1 (1996) 689-708
    • (1996) Adv. Differential Equations , vol.1 , pp. 689-708
    • Iliev, I.D.1
  • 12
    • 0030578195 scopus 로고    scopus 로고
    • The cyclicity of the period annulus of the quadratic Hamiltonian triangle
    • I.D. Iliev The cyclicity of the period annulus of the quadratic Hamiltonian triangle J. Differential Equations 128 (1996) 309-326
    • (1996) J. Differential Equations , vol.128 , pp. 309-326
    • Iliev, I.D.1
  • 13
    • 0032020006 scopus 로고    scopus 로고
    • Perturbations of quadratic centers
    • I.D. Iliev Perturbations of quadratic centers Bull. Sci. Math. 122 (1998) 107-161
    • (1998) Bull. Sci. Math. , vol.122 , pp. 107-161
    • Iliev, I.D.1
  • 14
    • 34250133017 scopus 로고
    • Real analytic manifolds with the property of finiteness and complex abelian integrals
    • A. Khovanskii Real analytic manifolds with the property of finiteness and complex abelian integrals Funct. Anal. Appl. 18 (1984) 119-127
    • (1984) Funct. Anal. Appl. , vol.18 , pp. 119-127
    • Khovanskii, A.1
  • 15
    • 30944458246 scopus 로고    scopus 로고
    • A unified study on the cyclicity of period annulus of the reversible quadratic Hamiltonian systems
    • C. Li J. Llibre A unified study on the cyclicity of period annulus of the reversible quadratic Hamiltonian systems J. Dyn. Differential Equations 16 (2004) 271-295
    • (2004) J. Dyn. Differential Equations , vol.16 , pp. 271-295
    • Li, C.1    Llibre, J.2
  • 16
    • 0042974314 scopus 로고    scopus 로고
    • Remarks on 16th weak Hilbert problem for n=2
    • C. Li Z.-H. Zhang Remarks on 16th weak Hilbert problem for n = 2 Nonlinearity 15 (2002) 1975-1992
    • (2002) Nonlinearity , vol.15 , pp. 1975-1992
    • Li, C.1    Zhang, Z.-H.2
  • 17
    • 0012779104 scopus 로고    scopus 로고
    • Limit cycles of perturbations of a class of quadratic Hamiltonian vector fields
    • Ya. Markov Limit cycles of perturbations of a class of quadratic Hamiltonian vector fields Serdica Math. J. 22 (1996) 91-108
    • (1996) Serdica Math. J. , vol.22 , pp. 91-108
    • Markov, Ya.1
  • 18
    • 51249171477 scopus 로고    scopus 로고
    • On the number of limit cycles which appear by perturbation of separate loop of planar vector fields
    • R. Roussarie On the number of limit cycles which appear by perturbation of separate loop of planar vector fields Bol. Soc. Bras. Mat. 17 (1996) 67-101
    • (1996) Bol. Soc. Bras. Mat. , vol.17 , pp. 67-101
    • Roussarie, R.1
  • 19
    • 84968514049 scopus 로고
    • Algebraic particular integrals, integrability and the problem of the center
    • D. Schlomiuk Algebraic particular integrals, integrability and the problem of the center Trans. Amer. Math. Soc. 338 (1993) 799-841
    • (1993) Trans. Amer. Math. Soc. , vol.338 , pp. 799-841
    • Schlomiuk, D.1
  • 20
    • 0002232057 scopus 로고
    • Estimation of the number of zeros of an abelian integral depending on a parameter and limit cycles
    • A.N. Varchenko Estimation of the number of zeros of an abelian integral depending on a parameter and limit cycles Funct. Anal. Appl. 18 (1984) 98-108
    • (1984) Funct. Anal. Appl. , vol.18 , pp. 98-108
    • Varchenko, A.N.1
  • 21
    • 30944434893 scopus 로고    scopus 로고
    • Qualitative theory of ordinary differential equations and tangential Hilbert 16th problem
    • Montreal
    • S. Yakovenko, Qualitative theory of ordinary differential equations and tangential Hilbert 16th problem, CRM Proceedings and Lecture Notes, (2004) Montreal.
    • (2004) CRM Proceedings and Lecture Notes
    • Yakovenko, S.1
  • 22
    • 0003264465 scopus 로고
    • Theory of Limit Cycles
    • Monographs, No. 66 Providence, RI
    • Y. Ye, Theory of Limit Cycles, Monographs, No. 66, Trans. Math. Amer. Math. Soc., Providence, RI, (1986).
    • (1986) Trans. Math. Amer. Math. Soc.
    • Ye, Y.1
  • 23
    • 0010203841 scopus 로고
    • On the number of limit cycles of a class of quadratic Hamiltonian systems under quadratic perturbations
    • Z. Zhang C. Li On the number of limit cycles of a class of quadratic Hamiltonian systems under quadratic perturbations Res. Rep. 33 (1993)
    • (1993) Res. Rep. , vol.33
    • Zhang, Z.1    Li, C.2
  • 24
    • 0012823734 scopus 로고
    • On the number of limit cycles of a class of quadratic Hamiltonian systems under quadratic perturbations
    • Z. Zhang C. Li On the number of limit cycles of a class of quadratic Hamiltonian systems under quadratic perturbations Adv. in Math. 26 (1987) 445-460
    • (1987) Adv. in Math. , vol.26 , pp. 445-460
    • Zhang, Z.1    Li, C.2
  • 25
    • 0034688727 scopus 로고    scopus 로고
    • The cyclicity of period annulus of the quadratic Hamiltonian systems with non-Morsean point
    • Y. Zhao Z. Liang G. Lu The cyclicity of period annulus of the quadratic Hamiltonian systems with non-Morsean point J. Differential Equations 162 (2000) 199-223
    • (2000) J. Differential Equations , vol.162 , pp. 199-223
    • Zhao, Y.1    Liang, Z.2    Lu, G.3
  • 26
    • 0035256188 scopus 로고    scopus 로고
    • Perturbations of the non-generic quadratic Hamiltonian vector fields with hyperbolic segment
    • Y. Zhao Z. Zhu Perturbations of the non-generic quadratic Hamiltonian vector fields with hyperbolic segment Bull. Sci. Math. 125 (2001) 109-138
    • (2001) Bull. Sci. Math. , vol.125 , pp. 109-138
    • Zhao, Y.1    Zhu, Z.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.