  We apply an operator-theoretic viewpoint to a class of non-smooth dynamical
systems that are exposed to event-triggered state resets. The considered
benchmark problem is that of a pendulum which receives a downward kick under
certain fixed angles. The pendulum is modeled as a hybrid automaton and is
analyzed from both a geometric perspective and the formalism carried out by
Koopman operator theory. A connection is drawn between these two
interpretations of a dynamical system by means of establishing a link between
the spectral properties of the Koopman operator and the geometric properties in
the state-space.
