Bifurcations of subharmonic solutions in periodic perturbation of a hyperbolic limit cycle. (Q1861066)

Consider the planar periodically perturbed system \[ \dot x= f(x)+ \varepsilon g(t,x,\varepsilon,\delta),\quad x\in\mathbb{R}^2,\tag{1} \] where \(\varepsilon\in \mathbb{R}\), \(\delta\in \mathbb{R}^n\), \(f\) and \(g\) are \(C^3\)-functions and \(g\) is \(T\)-periodic in \(t\). Suppose that for \(\varepsilon= 0\) system (1) has a family of periodic orbits of period \(T_0\). Suppose that \(T_0/T\) is rational, that is \(T_0/T= {m\over k}\), \((m,k)= 1\). The authors study the existence of harmonic \((m=1)\) and subharmonic \((m> 0)\) solutions bifurcating from the family of periodic orbits of the unperturbed system.