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Introduction to the Perturbation Theory of Hamiltonian Systems [electronic resource] / by Dmitry Treschev, Oleg Zubelevich.

By: Treschev, Dmitry [author.].
Contributor(s): Zubelevich, Oleg [author.] | SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Springer Monographs in Mathematics: Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2010Description: X, 211p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783642030284.Subject(s): Mathematics | Global analysis (Mathematics) | Differentiable dynamical systems | Topology | Mechanics | Mathematics | Dynamical Systems and Ergodic Theory | Analysis | Topology | MechanicsDDC classification: 515.39 | 515.48 Online resources: Click here to access online
Contents:
Hamiltonian Equations -- to the KAM Theory -- Splitting of Asymptotic Manifolds -- The Separatrix Map -- Width of the Stochastic Layer -- The Continuous Averaging Method -- The Anti-Integrable Limit -- Hill’s Formula.
In: Springer eBooksSummary: This book presents the basic methods of regular perturbation theory of Hamiltonian systems, including KAM-theory, splitting of asymptotic manifolds, the separatrix map, averaging, anti-integrable limit, etc. in a readable way. Although concise, it discusses all main aspects of the basic modern theory of perturbed Hamiltonian systems and most results are given with complete proofs. It will be a valuable reference for Hamiltonian systems, and of special interest to researchers and graduate students of the KAM community.
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Hamiltonian Equations -- to the KAM Theory -- Splitting of Asymptotic Manifolds -- The Separatrix Map -- Width of the Stochastic Layer -- The Continuous Averaging Method -- The Anti-Integrable Limit -- Hill’s Formula.

This book presents the basic methods of regular perturbation theory of Hamiltonian systems, including KAM-theory, splitting of asymptotic manifolds, the separatrix map, averaging, anti-integrable limit, etc. in a readable way. Although concise, it discusses all main aspects of the basic modern theory of perturbed Hamiltonian systems and most results are given with complete proofs. It will be a valuable reference for Hamiltonian systems, and of special interest to researchers and graduate students of the KAM community.

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