COMMUTING SINGULAR VECTOR FIELDS WITH LINEAR PARTS HAVING JORDAN BLOCKS

ABSTRACT. We consider the problem of the simultaneous lineariza-tion of commuting singular analytic vector fields in Kn, $\mathrm{K}=\mathbb{C},\mathrm{R}$, with non-semisimple linear parts. We investigate the solvability under compatibility conditions of overdetermined systems of lin-ear homological equations. We also examine the influence of the presence of Jordan blocks for intersections of foliations defined by two commuting real vectors fields in $\mathbb{R}^{2n} $ with odd-dimensional spheres. Key words: commuting singular vector fields, simultaneous lineariza-tion, Jordan blocks, homological equations, Diophantine conditions, transversal intersection