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Exponentially Small Lower Bounds for the Splitting of Separatrices to Whiskered Tori with Frequencies of Constant Type
We study the splitting of invariant manifolds of whiskered tori with two frequencies in nearly-integrable Hamiltonian systems, such that the hyperbolic part is given by a pendulum. We consider a two-dimensional torus with a fast frequency vector [Formula: see text], with ω = (1, Ω) where Ω is an irrational …