Locating invariant tori for a family of two-dimensional Hamiltonian mappings

The location of invariant tori for a two-dimensional Hamiltonian mapping exhibiting mixed phase space is discussed. The phase space of the mapping shows a large chaotic sea surrounding periodic islands and limited by a set of invariant tori. Given the mapping considered is parameterised by an exponent γ in one of the dynamical variables, a connection with the standard mapping near a transition from local to global chaos is used to estimate the position of the invariant tori limiting the size of the chaotic sea for different values of the parameter γ.