Stability properties of periodic solutions of periodically forced non-degenerate systems
Alan R. Hausrath, Raul F Manasevich · Rocky Mountain Journal of Mathematics · 1988
In this paper we study the stability properties of T-periodic solutions of the ordinary differential equation (1.1)x' = f(x) + eF (t,x) where ' denotes ^ and s G R is a small parameter.We make the following hypotheses about (1.1):that is, there exists a continuum C of periodic orbits of (1.2) contained in U and enclosing the origin.Moreover, C contains a nontrivial periodic solution of least period T which will be denoted by u.4. w is non-degenerate where we define non-degenerate periodic solutions as follows.Let v be a nontrivial (/-periodic solution of (1.2).Associated with (1.2) and v we have the linear variational equation (1-3) y' = Uv(t))y,