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Volumn 115, Issue , 2000, Pages 269-284

On the limit cycles available from polynomial perturbations of the Bogdanov-Takens Hamiltonian

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EID: 0034355417     PISSN: 00212172     EISSN: 15658511     Source Type: Journal    
DOI: 10.1007/BF02810590     Document Type: Article
Times cited : (28)

References (11)
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    • (1977) Functional Analysis and Applications , vol.11 , pp. 85-92
    • Arnol'd, V.I.1
  • 2
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    • Successive derivatives of a first return map, application to the study of quadratic vector fields
    • J.-P. Françoise, Successive derivatives of a first return map, application to the study of quadratic vector fields, Ergodic Theory and Dynamical Systems 16 (1996), 87-96.
    • (1996) Ergodic Theory and Dynamical Systems , vol.16 , pp. 87-96
    • Françoise, J.-P.1
  • 3
    • 0000047477 scopus 로고    scopus 로고
    • The first derivative of the period function of a plane vector field
    • J.-P. Françoise, The first derivative of the period function of a plane vector field, Publicacions Matematiques 41 (1997), 127-134.
    • (1997) Publicacions Matematiques , vol.41 , pp. 127-134
    • Françoise, J.-P.1
  • 4
    • 0001722685 scopus 로고    scopus 로고
    • Higher-order Melnikov functions for degenerate cubic Hamiltonians
    • I. D. Iliev, Higher-order Melnikov functions for degenerate cubic Hamiltonians, Advances in Differential Equations 1 (1996), 689-708.
    • (1996) Advances in Differential Equations , vol.1 , pp. 689-708
    • Iliev, I.D.1
  • 6
    • 0001530918 scopus 로고
    • A note on a result of G. S. Petrov about the weakened 16th Hubert problem
    • Bao-yi Li and Zhi-fen Zhang, A note on a result of G. S. Petrov about the weakened 16th Hubert problem, Journal of Mathematical Analysis and Applications 190 (1995), 489-516.
    • (1995) Journal of Mathematical Analysis and Applications , vol.190 , pp. 489-516
    • Li, B.-Y.1    Zhang, Z.-F.2
  • 7
    • 0000669485 scopus 로고
    • The number of limit cycles of polynomial deformations of a Hamiltonian vector field
    • P. Mardešić, The number of limit cycles of polynomial deformations of a Hamiltonian vector field, Ergodic Theory and Dynamical Systems 10 (1990), 523-529.
    • (1990) Ergodic Theory and Dynamical Systems , vol.10 , pp. 523-529
    • Mardešić, P.1
  • 8
    • 0001799622 scopus 로고
    • On the number of zeros of complete elliptic integrals
    • in Russian
    • G. S. Petrov, On the number of zeros of complete elliptic integrals, Functional Analysis and Applications 18 (1984), no 2, 73-74 (in Russian).
    • (1984) Functional Analysis and Applications , vol.18 , Issue.2 , pp. 73-74
    • Petrov, G.S.1
  • 9
    • 0001888120 scopus 로고
    • Elliptic integrals and their non-oscillatorness
    • in Russian
    • G. S. Petrov, Elliptic integrals and their non-oscillatorness, Functional Analysis and Applications 20 (1986), no 1, 46-49 (in Russian).
    • (1986) Functional Analysis and Applications , vol.20 , Issue.1 , pp. 46-49
    • Petrov, G.S.1
  • 11
    • 0000187914 scopus 로고
    • A geometric proof of the Bautin theorem
    • Concerning the Hilbert 16th Problem, American Mathematical Society, Providence
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    • Yakovenko, S.1


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