Abstract

This chapter reviews complete integrability in the setting of Lagrangian/Hamiltonian mechanics. It includes the construction of angle-action variables in illustrative examples, along with a proof of the Liouville-Arnol'd theorem. Results on the topology of the configuration space of a mechanical (or Tonelli) Hamiltonian are reviewed and several open problems are high-lighted.

Mathematics Subject Classication (2010): 37J30; 53C17, 53C30, 53D25

Keywords: Hamiltonian mechanics, Lagrangian mechanics, integrability, topological obstructions, topological entropy
