Isolating segments, fixed point index, and symbolic dynamics
The authors extend the method of \textit{R. Srzednicki} and \textit{K. Wójcik} [J. Differ. Equations 135, No.~1, 66-82 (1997; Zbl 0873.58049)] for the detection of chaotic dynamics in periodically forced ordinary differential equations. Their method is based on checking the so-called topological hyperbolicity by construction of periodic isolating segments. As an example, they show that the following planar system (written in the complex form) \[ z'=\left(1+e^{ikt}|z|^2\right)z \] has a symbolic dynamics on three symbols for \(0<k<0.495\).
periodically forced ordinary differential equations
scientific article; zbMATH DE number 1437327