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 R-n , n less than or equal to 5, with only two kinds of exceptions, any two hyperbolic vector fields with generic nonlinear parts x = A(1)x + (. . .) and y = A(1)y + (. . .), where A(i) are n x n matrices, are C-1 conjugate to each other if and only if A(1) and A(2) are strictly similar, and they are C-1 orbitally equivalent if and only if A(1) and A(2) are similar. (C) 2003 Elsevier Inc. All fights reserved.