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Hamiltonian systems with orbits covering densely submanifolds of small codimension
Fontich i Julià, Ernest; Martín de la Torre, Pablo
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
The existence of a transition chain in a Hamiltonian system leads to the existence of orbits shadowing it, if some lambda lemma can be applied. This fact has been used to prove the existence of diffusion in perturbations of integrable a priori stable systems. We prove that, under suitable conditions, there are orbits which cover densely codimension two submanifolds of the (2n - 1)-dimensional energy level. We also construct examples, near general integrable systems, where the computations to verify the sufficient conditions for the appearance of such phenomenon can be performed.
Dynamical systems
Hamiltonian dynamical systems
Lagrangian functions
Hamiltonian systems
invariant tori
Arnold diffusion
Hamilton, Sistemes de
Lagrange, Funcions de
Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics
Attribution-NonCommercial-NoDerivs 2.5 Spain
http://creativecommons.org/licenses/by-nc-nd/2.5/es/
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