Linearization of isochronous centers
The authors propose a unified technique for the study of the isochronicity of polynomial systems. They first construct the linearizing changes of coordinates for isochronous systems having rational first integrals, namely for quadratic systems, for cubic systems symmetric with respect to a center and for reduced Kukles systems. Further, other two classes of systems with isochronous centers having a Darboux first integral are studied, namely cubic systems symmetric with respect to the line and satisfying \(\dot\Theta= 1\) and the class of systems \(\dot z= iP(z)\), for which the authors derive the linearizing changes of coordinates and discuss their geometric properties. Some geometric properties of the linearizing change of coordinates for a system with a rational first integral in the complex plane are discussed and a number of open question for further research is posed.
scientific article; zbMATH DE number 800402