Periodic Orbits and Invariant Tori from a Semistable Limit Cycle in the Fast Dynamics

IntroductionIn the paper,the bifurcations of periodic or-bits and invariant tori of the following system wasstudied:x。=f(x,y) εh(t,x,y,ε)∈R2y。=εg(t,x,y,ε)∈R,0≤ε1(1)where h(t,x,y,ε)and g(t,x,y,ε)are T-periodicin t.For simplicity,the functions f,g and h areassumed to be sufficiently smooth in their argu-ments throughout this paper.In Ref.[1],Wiggins and Holmes called thesystems of form Eq.(1)as slowly varying oscilla-tors and pointed out that the systems taking theform occur as mo…