On C1 classifications of hyperbolic vector fields

In this paper we study smooth classification of hyperbolic vector fields based on their linear approximations only and obtain the following. On Rn, n 5, with only two kinds of exceptions, any two hyperbolic vector fields with generic nonlinear parts ˙x = A1x +··· and ˙y = A1y +···, where Ai are n × n matrices, are C1 conjugate to each other if and only if A1 and A2 are strictly similar, and they are C1 orbitally equivalent if and only if A1 and A2 are similar.  2003 Elsevier Inc. All rights reserved