数学物理学报(英文版) ›› 2001, Vol. 21 ›› Issue (1): 29-36.

• 论文 • 上一篇    下一篇

THE INVARIANT CLOSED CONES OF HOMOGENEOUS VECTOR FIELDS OF DEGREE TWO IN R3

 梁肇军, B.D.Sleeman   

  1. Department of Mathematics, Central China Normal University, Wuhan 430079, China The School of Mthematics, Department of Applied Mathematical Studies,
    The University of Leeds, Leeds LS2 9JT U.K.
  • 出版日期:2001-01-06 发布日期:2001-01-06
  • 基金资助:

    Project supported by the NNSF of China

THE INVARIANT CLOSED CONES OF HOMOGENEOUS VECTOR FIELDS OF DEGREE TWO IN R3

 LIANG Zhao-Jun, B.D.Sleeman   

  1. Department of Mathematics, Central China Normal University, Wuhan 430079, China The School of Mthematics, Department of Applied Mathematical Studies,
    The University of Leeds, Leeds LS2 9JT U.K.
  • Online:2001-01-06 Published:2001-01-06
  • Supported by:

    Project supported by the NNSF of China

摘要:

In this paper, we investigate the invariant cones of quadratic homogeneous polynomial vector fields in three variables. Necessary and sufficient conditions for the existence of non-isolated invariant closed cones are obtained by the algebraic expressions in terms of the coefficients of certain quadratic homogeneous polynomials.

关键词: Homogeneous vector field, invariant cone

Abstract:

In this paper, we investigate the invariant cones of quadratic homogeneous polynomial vector fields in three variables. Necessary and sufficient conditions for the existence of non-isolated invariant closed cones are obtained by the algebraic expressions in terms of the coefficients of certain quadratic homogeneous polynomials.

Key words: Homogeneous vector field, invariant cone

中图分类号: 

  • 34C35