Hamiltonian Systems
Dynamics, Analysis, Applications

A selection of results, spanning a broad spectrum of disciplines, from the MSRI program on Hamiltonian Systems during Fall 2018.

Albert Fathi (Edited by), Philip J. Morrison (Edited by), Tere M-Seara (Edited by), Sergei Tabachnikov (Edited by)

9781009320719, Cambridge University Press

Hardback, published 9 May 2024

376 pages
24 x 16.3 x 2.5 cm, 0.71 kg

Dynamical systems that are amenable to formulation in terms of a Hamiltonian function or operator encompass a vast swath of fundamental cases in applied mathematics and physics. This carefully edited volume represents work carried out during the special program on Hamiltonian Systems at MSRI in the Fall of 2018. Topics covered include KAM theory, polygonal billiards, Arnold diffusion, quantum hydrodynamics, viscosity solutions of the Hamilton–Jacobi equation, surfaces of locally minimal flux, Denjoy subsystems and horseshoes, and relations to symplectic topology.

1. Denjoy subsystems and horseshoes Marie-Claude Arnaud
2. Impact Hamiltonian systems and polygonal billiards L. Becker, S. Elliott, B. Firester, S. Gonen Cohen, Michael Pnueli and Vered Rom-Kedar
3. Some remarks on the classical KAM theorem, following Pöschel Abed Bounemoura
4. Some recent developments in Arnold diffusion Chong-Qing Cheng and Jinxin Xue
5. Viscosity solutions of the Hamilton–Jacobi equation on a noncompact manifold Albert Fathi
6. Holonomy and vortex structures in quantum hydrodynamics Michael S. Foskett and Cesare Tronci
7. Surfaces of locally minimal flux Robert S. MacKay
8. A symplectic approach to Arnold diffusion problems Jean-Pierre Marco
9. Hamiltonian ODE, homogenization, and symplectic topology Fraydoun Rezakhanlou.

Subject Areas: Calculus & mathematical analysis [PBK]