On the autonomous norm on the group of Hamiltonian diffeomorphisms of the torus

We prove that the autonomous norm on the group of Hamiltonian diffeomorphisms of the two-dimensional torus is unbounded. We provide examples of Hamiltonian diffeomorphisms with arbitrarily large autonomous norm. For the proofs we construct explicit quasimorphisms on Ham(T-2), some of them are C-0-continuous and vanish on all autonomous diffeomorphisms, and some of them are Calabi.