### Mixing in non-monotonic piecewise-linear toral maps

Ergodic Theory and Dynamical Systems Seminar

14th March 2024, 2:00 pm – 3:00 pm

Fry Building, G.07

We consider a family of area-preserving toral maps, each given by the composition of horizontal and vertical shears. These can be viewed as simplified stroboscopic maps of `eggbeater’ flows, modelling the stretching and folding dynamics of laminar fluid mixing. We give conditions for three key behaviours (mixing via hyperbolicity, unmixing, intermittency) and discuss the challenges in proving ergodic properties. Using results from the chaotic billiards literature, we show (strong, measure-theoretic) mixing properties and bounds on decay of correlations over a broad parameter space. This includes fast mixers where the decay rate is exponential, alongside other examples where intermittency slows the mixing to a polynomial rate.

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