An operator-theoretic viewpoint to non-smooth dynamical systems: Koopman   analysis of a hybrid pendulum
  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. 
Nithin Govindarajan, Hassan Arbabi, Louis van Blargian, Timothy   Matchen, Emma Tegling and Igor Mezi\'c
math.DS