THE ISOCHRONOUS CENTER PROBLEM FOR TIME REVERSIBLE SYSTEMS
时间可逆系统的等时中心问题

A center is called an isochronous center if those periodic orbits in some neighbourhood have the same period. The isochronous center problem for polynomial systems is an open problem. In order to solve it in constructive way, a class of time-reversible analytic dynamical systems is considered, for which recurrence formulae are proposed for deducing corresponding transversal commuting systems, which is helpful for constructing isochronous center conditions. For a class of time-reversible cubic systems, the necessary and sufficent conditions for having transversal commuting systems are obtained by Wu Characteristic-Sets method and formulae.