Acta mathematica scientia,Series B ›› 2001, Vol. 21 ›› Issue (1): 29-36.

• Articles • Previous Articles     Next Articles

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

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

CLC Number: 

  • 34C35
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