INVARIANT SURFACES OF TWO-DIMENSIONAL PERIODIC SYSTEMS WITH BIFURCATING REST POINTS IN THE FIRST APPROXIMATION

摘要

Two-dimensional, time-periodic systems of differential equations with a small positive parameter whose first-approximation systems are conservative, depend on the parameter, and have one, two, or three rest points are considered. Explicit conditions on the coefficients under which the initial system has one or several two-dimensional invariant surfaces homeomorphic to the torus for all sufficiently small parameter values are obtained, and formulas for these surfaces are presented. As an example, a class of systems with three two-periodic invariant surfaces is constructed.