Center problem and bifurcation behavior for a class of quasi analytic systems
The authors discuss a class of quasi-analytic systems depending on a parameter from the viewpoint of determining whether a nondegenerate critical point is a center or a weak focus (the center-focus problem) and whether or not the limit cycles bifurcate. A reduction theorem is obtained by means of a formal series expansion, being shown that the origin (or the singular point at infinity) is a center (a isochronous center) if and only if the origin of an associated analytic system is a center (an isochronous center). As an example, the center-focus and bifurcation problem of a class of quasi-analytic cubic systems is studied, a recursive formula to determine the generalized focal values being obtained.
quasi analytic planar differential system
scientific article; zbMATH DE number 5843691