Analytic diffeomorphisms as monodromy transforms of analytic differential equations (Q1091517)

This note discusses the problem of including the analytic diffeomorphisms of compact manifolds in the flow of analytic vector fields as transformations of monodromy. The result is: Let M be a compact analytic manifold, \(\Delta\) : \(M\to M\) an analytic diffeomorphism, smoothly homotopic to identity, then there exists an analytic vector field v on \(M\times S^ 1=\{(x,t)|\) \(x\in M\), \(t\in R/2\pi Z\}\) for which the mapping \(\Delta\) is a transformation of monodromy on the section \(t=0\), i.e., point \(x\in M\) is brought to the first point, with respect to t after point (x,0), of intersection of manifold \(M\times \{0\}\) and the positive half-trajectory of the vector field v from the starting-point (x,0).