Huang Debin, Zhao Xiaohua. The Vector Fields Admitting One-Parameter Spatial Symmetry Group and Their Reduction[J]. Applied Mathematics and Mechanics, 2000, 21(2): 154-160.
Citation: Huang Debin, Zhao Xiaohua. The Vector Fields Admitting One-Parameter Spatial Symmetry Group and Their Reduction[J]. Applied Mathematics and Mechanics, 2000, 21(2): 154-160.

The Vector Fields Admitting One-Parameter Spatial Symmetry Group and Their Reduction

  • Received Date: 1997-01-20
  • Rev Recd Date: 1999-04-28
  • Publish Date: 2000-02-15
  • For a n-dimensional vector fields preserving some n-form,the following conclusion is reached by the method of Lie group.That is,if it admits a one-parameter,n-form preserving symmetry group,a transformation independent of the vector field is constructed explicitly,which can reduce not only dimesion of the vector field by one,but also make the reduced vector field preserve the corresponding(n-1)-form.In particular,while n=3,an important result can be directly got which is given by Mezie and Wiggins in 1994.
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  • [1]
    Olver P J.Applications of Lie Group to Differential Equations[M].New York:Springer-Verlag,1986.
    [2]
    Sen T,Tabor M.Lie symmetries of the Lorenz model[J].Physica D,1990,44(3):313~339.
    [3]
    Smale S.Topology and mechanics[J].Inv Math,1970,10(2):305~331.
    [4]
    Meyer K R.Symmetries and integrals in mechanics[A].In:M M Peixoto Ed.Dynamical Systems[C].New York:Academic Press,1973,259~272.
    [5]
    Marsden J E,Weinstein A.Reduction of symplectic manifolds with symmetry[J].Rep Math Phys,1974,5(1):121~130.
    [6]
    李继彬,赵晓华,刘正荣.广义哈密顿系统理论及其应用[M].北京:科学出版社,1994.
    [7]
    Mezie J,Wiggins S.On the integrability and perturbation of three-dimensional fluid flows with symmetry[J].J Nonlinear Science,1994,4(1):157~194.
    [8]
    Ottino J M.The Kinematics of Mixing:Stretching,Chaos and Transprot[M].Cambridge:Cambridge University Press,1989.
    [9]
    郭仲衡,陈玉明.具有不依赖于时间的不变量的三维常微分方程组的Hamilton结构[J].应用数学和力学,1995,16(4):283~288.
    [10]
    张景炎.三维梯度共轭系统的全周期性[J].中国科学A辑,1983,13(5):426~437.
    [11]
    Marsden J E,Ratiu T S.Introduction to Mechanics and Symmetry[M].New York:Springer-Verlag,1994.
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