Hamiltonian Systems

Andrew Fowler () and Mark McGuinness
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Andrew Fowler: University of Limerick, MACSI
Mark McGuinness: Victoria University of Wellington, School of Mathematics and Statistics

Chapter Chapter 5 in Chaos, 2019, pp 143-206 from Springer

Abstract: Abstract The chapter begins with the derivation of Hamilton’s equations for conservative mechanical systems, and discusses integrability and canonical transformations. Perturbation theory is described, and the essence of Arnold’s proof of the KAM theorem is given. The consequence of resonance is analysed, and the resulting occurrence of heteroclinic tangles and stochasticity is portrayed, using Melnikov’s method. A number of examples are then discussed and plentifully illustrated, including an extended description of the restricted three-body problem.

Date: 2019
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DOI: 10.1007/978-3-030-32538-1_5

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