Sobolev norms explosion for the cubic NLS on irrational tori

We consider the cubic nonlinear Schrödinger equation on 2-dimensional irrational tori. construct solutions which undergo growth of Sobolev norms. More concretely, for every s>0, s≠1 and almost choice spatial periods we whose Hs norms grow by any prescribed factor. Moreover, a set with positive Hausdorff dimension go from arbitrarily small to large. also provide estimates time needed norm explosion. Note that irrationality space decouples linear resonant interactions into products 1-dimensional resonances, reducing considerably complexity dynamics usually used transfer energy solutions. However, one can these using quasi-resonances relying Diophantine approximation properties periods.