Ke Min Zhang

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In the present paper we prove a strong form of Arnold diffusion. Let T 2 be the two torus and B 2 be the unit ball around the origin in R 2. Fix ρ > 0. Our main result says that for a " generic " time-periodic perturbation of an integrable system of two degrees of freedom H 0 (p) + εH 1 (θ, p, t), θ ∈ T 2 , p ∈ B 2 , t ∈ T = R/Z, with a strictly convex H 0(More)
In the present paper we prove a form of Arnold diffusion. The main result says that for a " generic " perturbation of a nearly integrable system of arbitrary degrees of freedom n 2 H 0 (p) + εH 1 (θ, p, t), θ ∈ T n , p ∈ B n , t ∈ T = R/T, with strictly convex H 0 there exists an orbit (θ ǫ , p e)(t) exhibiting Arnold diffusion in the sens that sup t>0 p(t)(More)
We study a C r nearly integrable Hamiltonian system Hε(q, p) = 1 2 p, p + H 1 (q, p) defined on T 3 × R 3. Let Σ = {(q, p) : Hε(q, p) = 1 2 } and µ Σ 1 be the restriction of Lebesgue measure on T 3 × R 3 to Σ. We prove there is a perturbation H 1 (q, p) ∈ C r , H 1 C r ≤ 1 and an orbit (q(t), p(t)) : R → T 3 × R 3 of the Hamiltonian equation { ˙ q = ∂pHε, ˙(More)
We present key elements of a proof of a strong form of Arnold diffusion for systems of three and a half degrees of freedom. More exactly, let T 3 be a 3-dimensional torus and B 3 be the unit ball around the origin in R 3. Fix ρ > 0. Our main result says that for a " generic " time-periodic perturbation of an integrable system of three degrees of freedom H 0(More)
In this paper we study existence of Normally Hyperbolic Invariant Laminations (NHIL) for a nearly integrable system given by the product of the pendulum and the rotator perturbed with a small coupling between the two. This example was introduced by Arnold [1]. Using a separatrix map, introduced in a low dimensional case by Zaslavskii-Filonenko [61] and(More)