The Bernoulli property for counter-twisting linked twist maps

Abstract

We prove the Bernoulli property for a class of counter-twisting linked twist maps. These compose orthogonal linear shears on the torus, orientated in the opposite sense to their co-twisting counterparts (where the shears reinforce one another). Compared to previous studies we focus on the parameter space corresponding to weak shears, near the critical parameter below which hyperbolicity is lost and the map is non-mixing. The approach developed to deal with this situation appears applicable to a broad range of non-uniformly hyperbolic examples.