Area-preserving dynamics that is not reversible

In this paper we address some global dynamical features in area-preserving dynamical systems on the plane 2 which obstruct the presence of a time-reversal symmetry that is a reflection. We show that in the case of flows, reversibility and non-reversibility are non-generic properties. In the case of maps we show that reversibility is a non-generic property by constructing an example of a persistently non-reversible area-preserving map.