On detecting of chaotic dynamics via isolating chains

Abstract

We show in the paper the method of isolating chains in proof of chaotic dynamics. It is based on the earlier notion of an isolating segment but gives more powerful tool for exploring dynamics of periodic ODE's. As an application we show that the processes generated by the equations in the complex plane $ \dot{z} = {\overline z}^k + e^{i\phi t} {\overline z}$, where $k\geq 3$ is an odd number and $\phi$ is close to $0$, has chaotic behaviour.