Bifurcations of Critical Orbits of SO(2)-invariant Fredholm Functionals at Critical Points with Double Resonances
作者: Yu. I. Sapronov E.V. Derunova
刊名: Global and Stochastic Analysis, 2015, Vol.2 (2)
来源数据库: Mind Reader Publications
关键词: CycleresonanceLyapunov-Schmidt methodbifurcationcircular symmetry.
原始语种摘要: In this paper we consider the problem of bifurcation of extremals of SO(2)-invariant (i.e., with circular symmetry) Fredholm functional near a steady-state point with a double-resonance (i.e., with two independent resonance relations). The main method of investigation is a variational modification of the Lyapunov-Schmidt reduction. It allows us to find a normal form of key functions of functionals. J. Mather’s condition on a finite determinacy of a smooth map germ gives a simpler representation of the key function. Further bifurcational analysis of branching extremals reduces the problem to analysis of boundary and corner singularities via the secondary reduction.
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  • invariant 不变量
  • variational 变化的
  • symmetry 对称
  • corner 弯曲软波导
  • point 
  • resonance 共振
  • consider 仔细考虑
  • reduction 减少
  • representation 表现
  • investigation 研究