Braid invariants and instability of periodic solutions of time-periodic 2-dimensional ODE's (Q1580014)

Consider a 2D ordinary differential equation of the form: (1) \(dx/dt= f(x,t)\) where \(f: \mathbb{R}^2\times \mathbb{R}\to \mathbb{R}^2\) is a Carathéodory map. The paper deals with the problem of the existence of unstable periodic solutions of (1). In contrast to the traditional approach to this problem the author presents a purely topological approach to the problem. His approach makes use of the braid invariant. Using the braid invariant the author defines an equivalence relation on the set of periodic solutions. It is shown that more than half of the equivalence classes contain unstable solutions.