Asymptotic expansion of the period function.
Let \(P\) be a polycycle (i.e., a connected union of singularities and joining them integral curves) of an analytic vector field in the plane. The author studies the return-time function \(T\) near \(P\). Conditions are given under which the asymptotic expansions of the function \(T\) and its derivative \(T'\) converge to these functions absolutely and uniformly. The results are applied, for example, to analytic vector fields having a Darboux integral and to systems with nilpotent centers and foci.
scientific article; zbMATH DE number 2002184
scientific article