WEAK MIXING PROPERTIES OF INTERVAL EXCHANGE TRANSFORMATIONS & TRANSLATION FLOWS

摘要

Let d 1. In this paper we show that for an irreducible permutation pi which is not a rotation, the set of [lambda] is an element of P-+(d)-1 such that the interval exchange transformation f([lambda], pi) is not weakly mixing does not have full Hausdorff dimension. We also obtain an analogous statement for translation flows. In particular, it strengthens the result of almost sure weak mixing proved by G. Forni and the first author in [2]. We adapt here the probabilistic argument developed in their paper in order to get some large deviation results. We then show how the latter can be converted into estimates on the Hausdorff dimension of the set of "bad" parameters in the context of fast decaying cocycles, following the strategy of [1].