论文信息 - VECTOR FIELDS IN ℝ2 WITH MAXIMAL INDEX

VECTOR FIELDS IN ℝ2 WITH MAXIMAL INDEX

We consider the method of Poincare to investigate the local index of vector fields in the plane. If m is the degree of the first non-zero jet, Xm, of the vector field X at an isolated zero, we explore the geometry of the pencil generated by the coordinate functions of Xm when the absolute value of the index of X, |ind (X)|, is m. We also find necessary and sufficient conditions for |ind (X)| to be m.

M. Ruas | A. C. Nabarro

[1] A. Cima,et al. On the Relation between Index and Multiplicity , 1998 .

[2] M. Ruas. On the degree of $C^l$-determinacy. , 1986 .

[3] Charles Terence Clegg Wall,et al. Finite Determinacy of Smooth Map‐Germs , 1981 .

[4] T. Kuo. On C0-sufficiency of jets of potential functions , 1969 .

[5] J. Mather,et al. Stability of $C^\infty $ mappings, III. Finitely determined map-germs , 1968 .

[6] M. Ruas,et al. Indices of Newton non-degenerate vector fields and a conjecture of Loewner for surfaces in R 4 : , 2001 .