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Homoclinic Bifurcations in Symmetric Unfoldings of a Singularity with Three-fold Zero Eigenvalue 被引量:1

Homoclinic Bifurcations in Symmetric Unfoldings of a Singularity with Three-fold Zero Eigenvalue
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摘要 In this paper we study the singularity at the origin with three–fold zeroeigenvalue for symmetric vector fields with nilpotent linear part and 3–jet C~∞–equivalent toy(partial deriv)/(partial deriv) + z(partial deriv)/(partial deriv)y + ax^2y (partialderiv)/(partial deriv)/z with a ≠ 0. We first obtain several subfamilies of the symmetric versalunfoldings of this singularity by using the normal form and blow–up methods under some conditions,and derive the local and global bifurcation behavior, then prove analytically the existence of theSilnikov homoclinic bifurcation for some subfamilies of the symmetric versal unfoldings of thissingularity, by using the generalized Melnikov methods of a homoclinic orbit to a hyperbolic ornon–hyperbolic equilibrium in a highdimensional space. In this paper we study the singularity at the origin with three–fold zeroeigenvalue for symmetric vector fields with nilpotent linear part and 3–jet C~∞–equivalent toy(partial deriv)/(partial deriv) + z(partial deriv)/(partial deriv)y + ax^2y (partialderiv)/(partial deriv)/z with a ≠ 0. We first obtain several subfamilies of the symmetric versalunfoldings of this singularity by using the normal form and blow–up methods under some conditions,and derive the local and global bifurcation behavior, then prove analytically the existence of theSilnikov homoclinic bifurcation for some subfamilies of the symmetric versal unfoldings of thissingularity, by using the generalized Melnikov methods of a homoclinic orbit to a hyperbolic ornon–hyperbolic equilibrium in a highdimensional space.
作者 JianHuaSUN
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2005年第1期65-80,共16页 数学学报(英文版)
基金 Project supported by the National Natural Science Foundation of China(No.10171044) the Foundation for University Key Teachers of the Ministry of Education 34C05,34C15,58F14,58F30
关键词 SINGULARITY Symmetric unfolding Homoclinic orbit Silnikov bifurcation Normal form Blow–up Generalized Mel'nikov methods Singularity Symmetric unfolding Homoclinic orbit Silnikov bifurcation Normal form Blow–up Generalized Mel'nikov methods
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  • 1S. Ib′an?ez,J.A. Rodr′iguez.Sil’nikov bifurcations in generic 4-unfoldings of a codimension-4 singularity[].J Di?erential Equations.1995
  • 2V.I. Arnold,,V.S. Afraimovich,,Yu S. Il’yashenko,L.P. Sil’nikov.Bifurcation theory[].Dynamical Systems V.1986
  • 3V.K. Melnikov.On the stability of the center for time periodic perturbations[].Transactions Moscow Mathematical Society.1964
  • 4P.J. Holmes.Averaging and chaotic motions in forced oscillations[].SIAM Journal on Applied Mathematics.1980
  • 5F. Takens.Unfoldings of certain singularities of vector fields: Generalized Hopf bifurcations[].J Di?erential Equations.1973
  • 6Yu,P.,Huseyin,K.Bifurcations associated with a three-fold zero eigenvalue[].Quarterly of Applied Mathematics.1988
  • 7Dumortier,F.,Kokubu,H.,Oka,H.A degenerate singularity generating geometric Lorenz attractors[].ErgodThand DynamSys.1995
  • 8Silnikov,L. P.A case of the existence of a denumerable set of periodic motions[].Soviet Mathematics Doklady.1965
  • 9Elphick,C.,Tirapegui,E.,Brachet,M.E.,Coullet,P.,Iooss,G.A simple global characterization for normal forms of singular vector fields[].Physica D Nonlinear Phenomena.1987

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