Mixing Properties and Poisson Limit Distribution for Some Baker Transformations with Intermittency

We study intermittent baker transformations whose expanding and contracting direction behaves as Manneville-Pomeau maps or some one-dimensional intermittent maps. According to these intermittent types, we show that such maps have polynomial or stretched exponential mixing for Hölder continuous functions. Furthermore we show that such maps satisfy the Poisson limit distribution, i.e. the distributions of the number of visits to a ball \(B(x, r)\) converge to Poisson distributions as the radius \(r \to 0\).