Notes on Hamiltonian Dynamical Systems (eBook, PDF)

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Starting with the basics of Hamiltonian dynamics and canonical transformations, this text follows the historical development of the theory culminating in recent results: the Kolmogorov-Arnold-Moser theorem, Nekhoroshev''s theorem and superexponential stability. Its analytic approach allows students to learn about perturbation methods leading to advanced results. Key topics covered include Liouville''s theorem, the proof of Poincare¿''s non-integrability theorem and the nonlinear dynamics in the neighbourhood of equilibria. The theorem of Kolmogorov on persistence of invariant tori and the the...

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