Necessary Properties of Boundary Degree Sets of Solutions to Linear Pfaff Systems

Abstract

Consider the linear Pfaff system ∂x/∂ti = Ai(t)x, x ∈ Rn, t = (t1, t2) ∈ R2 ≥1, i = 1, 2, (1) with continuously differentiable matrix functions A1(t) and A2(t) bounded in R2 ≥1 and satisfying the complete integrability condition [1, pp. 14–24; 2, pp. 16–26] ∂A1(t)/∂t2 + A1(t)A2(t) = ∂A2(t)/∂t1 + A2(t)A1(t), t ∈ R2 ≥1.