Titlebook: Symmetries, Topology and Resonances in Hamiltonian Mechanics; Valerij V. Kozlov Book 1996 Springer-Verlag Berlin Heidelberg 1996 Bewegungs

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https://doi.org/10.1007/978-3-642-78393-7Bewegungsintegral; Hamiltonian Mechanics; Hamiltonsche Systeme; Separatrixspaltung; Symmetriefelder; diff

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Introduction,In 1834 Hamilton represented the differential equations of classical mechanics, i.e., the Lagrange equations.in “canonical” form

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Nonintegrability of Hamiltonian Systems Close to Integrable Ones,We begin the consideration of the analytic obstacles to integrability with the analysis of Poincaré’s “basic problem of dynamics”. This problem deals with the Hamiltonian system whose Hamiltonian has the form

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Integration of Hamiltonian Systems, definition of integrability, we discover that many different definitions are possible and each of them is interesting from a certain theoretical point of view” (Birkhoff [23]). In this chapter we survey various approaches to the problem of integrability of Hamiltonian systems.

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