On detecting periodic solutions and chaos in the time periodically forced ODEs (Q5940158)

Consider the differential equation NEWLINE\[NEWLINEdx/dt= f(t,x)\tag{1}NEWLINE\]NEWLINE on a smooth manifold under the condition that \(f\) is \(T\)-periodic in \(t\) and such that the Cauchy problem for (1) has a unique solution. The aim of the paper is to derive conditions on \(f\) guaranteeing the occurrence of chaotic behavior (in the sense of shift dynamics) and the existence of infinitely many periodic solutions of (1). The approach is based on the existence of periodic isolating segments satisfying some topological conditions.