We consider the break-up of invariant tori in Hamiltonian systems
with two degrees of freedom with a frequency which belongs to a cubic field.
We define and construct renormalization-group transformations in order to
determine the threshold of the break-up of these tori. A first transformation is
defined from the continued fraction expansion of the frequency, and a second
one is defined with a fixed frequency vector in a space of Hamiltonians with
three degrees of freedom.