Invariant manifolds of periodic orbits for piecewise linear three‐dimensional systems

This paper analyses the existence of invariant manifolds of periodic orbits for a specific piecewise linear three‐dimensional system with two zones, whose linear parts share a pair of imaginary eigenvalues. This degenerate situation is obtained from the lack of controllability. The analysis proceeds by its reduction to a periodic one‐dimensional equation for which some results of the Ambrosetti–Prodi type are given.