Steppingstones in Hamiltonian dynamics

Abstract

Easy steps through essential Hamiltonian dynamics are outlined, from necessary definitions of Poisson brackets and canonical transformations, to a quick proof that Hamiltonian evolution is made by canonical transformations, the quickest proof of Liouville's theorem, and on to Poincare-Cartan integral invariants and completely integrable dynamics, making room, providing tools, and setting the stage for more recent developments.

15 pages, 2 figures, submitted to American Journal of Physics, refereed, revised, recommended for publication by referee

Cited by in corpus (2)

• Algebro-geometric integration of the Q1 lattice equation via nonlinear integrable symplectic maps
• Quasiperiodicity in time evolution of the Bloch vector under the thermal Jaynes-Cummings model