Affine‐periodic orbits for linear dynamical systems

摘要

We observe the relationship between forward bounded orbits and affine periodic orbits for infinite‐dimensional linear dynamical systems and prove a Massera type criterion, which asserts that a forward bounded orbit implies the existence of affine periodic orbits. Such an affine‐periodic orbit might be periodic, quasi(almost)‐periodic, or spiral one. We also give an analog for hybrid (switching) discrete dynamical systems.