Hyperbolicity and Averaging for the Srzednicki-Wójcik equation

Abstract

For the Srzednicki-Wójcik equation, the planar nonautonomous ODE parameterized by $\kappa \in \mathbb{R}$, $$z^{\prime }=\overline{z}(1+|z{|}^2\exp (i\kappa t)),z(t)\in \mathbb{C}$$ using averaging we show how the region of hyperbolicty grows with $|\kappa |$. Based on this we give bounds on the sizes of bounded orbits.