2014/02/07 by Amadeu Delshams, Marina Gonchenko, Pere Gutiérrez
Mathematics · #math.DS #msc:37J40 #msc:70H08
paper · pdf · doi:10.1142/s0218127414400112
12 pages, 1 figure. arXiv admin note: text overlap with arXiv:1306.0728
arxiv created 2014/02/07 · arxiv updated 2015/06/18
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 2-dimensional torus with a fast frequency vector ω/√ε, with ω=(1,Ω) where Ω is an irrational number of constant type, i.e. a number whose continued fraction has bounded entries. Applying the Poincaré-Melnikov method, we find exponentially small lower bounds for the maximal splitting distance between the stable and unstable invariant manifolds associated to the invariant torus, and we show that these bounds depend strongly on the arithmetic properties of the frequencies.