Reshaping Arnold tongues

Given the Hill's equation x¿+(¿+ßp(t)t)x=0, where ¿ and ß are parameters and p(t) is periodic. The Arnold's tongues are the unstable regions in the ¿-ß plane where the solutions of the Hill's equation are unbounded. We shall present some results about the reshaping of the Arnold's tongues varying p(t) by p¿(t)=¿(p(t)+¿(t)) where the term ¿f(t) acts as control parameter. We shall present the results for the Mathieu's equation.