These lectures touch upon two aspects of Hamiltonian mechanics. The first one (geometric) establishes fundamental role of symplectic geometry as the language of Hamiltonian mechanics. The second aspect (dynamical) exhibits the main problem in the domain, which is the interplay between regular and chaotic motion.
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Arnold, V. I. Mathematical methods of classical mechanics. Graduate Texts in Mathematics, 60. Springer, New York, 1989.
Arnold, V. I., Kozlov, V. V., Neishtadt, A. I. Mathematical aspects of classical and celestial mechanics. Encyclopaedia Math. Sci., 3, Springer, Berlin, 1993. Springer, Berlin, 1997.
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Treschev, D.V. (2008). Some aspects of finite-dimensional Hamiltonian dynamics. In: Craig, W. (eds) Hamiltonian Dynamical Systems and Applications. NATO Science for Peace and Security Series. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-6964-2_1
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DOI: https://doi.org/10.1007/978-1-4020-6964-2_1
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