Exponentially and non-exponentially small splitting of separatrices for the pendulum with a fast meromorphic perturbation
نویسندگان
چکیده
منابع مشابه
Exponentially and non-exponentially small splitting of separatrices for the pendulum with a fast meromorphic perturbation
In this paper we study the splitting of separatrices phenomenon which arises when one considers a Hamiltonian System of one degree of freedom with a fast periodic or quasiperiodic and meromorphic in the state variables perturbation. The obtained results are different from the previous ones in the literature, which mainly assume algebraic or trigonometric polynomial dependence on the state varia...
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Abstract. In this paper, we study the classical problem of the exponentially small splitting of separatrices of the rapidly forced pendulum. Firstly, we give an asymptotic formula for the distance between the perturbed invariant manifolds in the so-called singular case and we compare it with the prediction of Melnikov Theory. Secondly, we give exponentially small upper bounds in some cases in w...
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The splitting of separatrices for the standard-like maps is measured. For even entire perturbative potentials V (y) = P n2 V n y 2n such that b V (2) 6 = 0, where b V () = P n2 V n 2n?1 =(2n ? 1)! is the Borel transform of V (y), the following asymptotic formula for the area A of the lobes between the perturbed separatrices is established A = 8 b V (2)" e ? 2 =h h 1 + O(h 2) i (" = o(h 6 ln ?1 ...
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ژورنال
عنوان ژورنال: Nonlinearity
سال: 2012
ISSN: 0951-7715,1361-6544
DOI: 10.1088/0951-7715/25/5/1367