A Family of Non-Monotonic Toral Mixing Maps

Abstract We establish the mixing property for a family of Lebesgue measure preserving toral maps composed two piecewise linear shears, first which is non-monotonic. The serve as basic model ‘stretching and folding’ action in laminar fluid mixing, particular flows where boundary conditions give rise to non-monotonic flow profiles. can be viewed parameter space between well-known systems, Arnold’s Cat Map map due Cerbelli Giona, both possess finite Markov partitions straightforward prove properties. However, no such appear exist present family, so establishing properties requires different approach. In particular, we follow scheme Katok Strelcyn, proving strong with respect on open spaces. Finally, comment challenges extending these windows potential using same approach similar systems.