메뉴 건너뛰기




Volumn 30, Issue 8, 1997, Pages 4789-4798

Uniqueness of limit cycles and quotients of abelian integrals

Author keywords

Abelian integral; Family of closed orbits; Limit cycle; Lotka Volterra system; Perturbation

Indexed keywords


EID: 0041726930     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(96)00361-6     Document Type: Article
Times cited : (1)

References (16)
  • 2
    • 0001048892 scopus 로고
    • Abelian integrals and bifurcation theory
    • CARR J., CHOW S.-N. & HALE J. K., Abelian integrals and bifurcation theory, J. Diff. Equations 59, 413-436 (1985).
    • (1985) J. Diff. Equations , vol.59 , pp. 413-436
    • Carr, J.1    Chow, S.-N.2    Hale, J.K.3
  • 3
    • 0001763980 scopus 로고
    • Limit cycles of perturbations of quadratic hamiltonian vector fields
    • GAVRILOV L. & HOROZOV E., Limit cycles of perturbations of quadratic hamiltonian vector fields, J. Math. Pures Appl. 72, 213-238 (1993).
    • (1993) J. Math. Pures Appl. , vol.72 , pp. 213-238
    • Gavrilov, L.1    Horozov, E.2
  • 4
    • 0010098877 scopus 로고
    • An inhomogeneous picard-fuchs equation
    • (Edited by P. CHOSSAT), Kluwer, Dordrecht Boston London
    • VAN GILS S. A., An inhomogeneous Picard-Fuchs equation, in Dynamics, bifurcation and symmetry (Edited by P. CHOSSAT), pp. 333-341. Kluwer, Dordrecht Boston London (1994).
    • (1994) Dynamics, Bifurcation and Symmetry , pp. 333-341
    • Van Gils, S.A.1
  • 5
    • 0003739973 scopus 로고
    • Multiparameter bifurcation of a predator-prey system
    • HAINZL J., Multiparameter bifurcation of a predator-prey system, SIAM J. Math. Anal. 23, 150-180 (1992).
    • (1992) SIAM J. Math. Anal. , vol.23 , pp. 150-180
    • Hainzl, J.1
  • 6
    • 85033114339 scopus 로고    scopus 로고
    • On the number of limit cycles in perturbations of the system ẋ = y, ẏ = - X + xy
    • To appear
    • HAINZL J., On the number of limit cycles in perturbations of the system ẋ = y, ẏ = - x + xy, Aequationes mathematicae. To appear.
    • Aequationes Mathematicae
    • Hainzl, J.1
  • 7
    • 0042302098 scopus 로고
    • Zeros of special abelian integrals in a real domain
    • IL'YASHENKO YU. S., Zeros of special abelian integrals in a real domain, Funct. Anal. and Appl. 11, 309-311 (1977).
    • (1977) Funct. Anal. and Appl. , vol.11 , pp. 309-311
    • Il'yashenko, Yu.S.1
  • 8
    • 84956229471 scopus 로고
    • On the versality of a family of symmetric vector fields in the plane
    • ŻOLADEK H. (ZHOLONDEK K.), On the versality of a family of symmetric vector fields in the plane, Math. Sborn. 48, 463-492 (1984).
    • (1984) Math. Sborn. , vol.48 , pp. 463-492
    • Zoladek, H.1    Zholondek, K.2
  • 9
    • 0012827513 scopus 로고
    • Abelian integrals in unfoldings of codimension 3 singular planar vector fields
    • Bifurcations of planar vector fields (F. DUMORTIER, R. ROUSSARIE, J. SOTOMAYOR, H. ŻOLADEK), Springer, Berlin Heidelberg
    • ŻOLADEK H., Abelian integrals in unfoldings of codimension 3 singular planar vector fields, in Bifurcations of planar vector fields (F. DUMORTIER, R. ROUSSARIE, J. SOTOMAYOR, H. ŻOLADEK), Lecture Notes in Math. 1480, pp. 165-224. Springer, Berlin Heidelberg (1991).
    • (1991) Lecture Notes in Math. , vol.1480 , pp. 165-224
    • Zoladek, H.1
  • 10
    • 0001686233 scopus 로고    scopus 로고
    • A criterion for determining the monotonicity of the ratio of two abelian integrals
    • LI C. & ZHANG Z.-F., A criterion for determining the monotonicity of the ratio of two abelian integrals, J. Diff. Equations 124, 407-424 (1996).
    • (1996) J. Diff. Equations , vol.124 , pp. 407-424
    • Li, C.1    Zhang, Z.-F.2
  • 11
    • 0001520613 scopus 로고
    • Bifurcation of limit cycles in a particular class of quadratic systems with two centres
    • VAN HORSSEN W. T. & KOOIJ R. E., Bifurcation of limit cycles in a particular class of quadratic systems with two centres, J. Diff. Equations 114, 538-569 (1994).
    • (1994) J. Diff. Equations , vol.114 , pp. 538-569
    • Van Horssen, W.T.1    Kooij, R.E.2
  • 13
    • 0000813963 scopus 로고
    • Quadratic systems with center and their perturbations
    • ŻOLADEK H., Quadratic systems with center and their perturbations, J. Diff. Equations 109, 223-273 (1994).
    • (1994) J. Diff. Equations , vol.109 , pp. 223-273
    • Zoladek, H.1
  • 14
    • 0038884337 scopus 로고
    • On saddle-loop bifurcations of limit cycles in perturbations of quadratic hamiltonian systems
    • HOROZOV E. & ILIEV I. D., On saddle-loop bifurcations of limit cycles in perturbations of quadratic hamiltonian systems, J. Diff. Equations 113, 84-105 (1994).
    • (1994) J. Diff. Equations , vol.113 , pp. 84-105
    • Horozov, E.1    Iliev, I.D.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.