Hamiltonian Systems
Hamiltonian Systems
Dynamics, Analysis, Applications
Albert Fathi, Georgia Institute of Technology
Philip J. Morrison, University of Texas, Austin
Tere M-Seara, Universitat Politècnica de Catalunya, Barcelona
Sergei Tabachnikov, Pennsylvania State University
Philip J. Morrison, University of Texas, Austin
Tere M-Seara, Universitat Politècnica de Catalunya, Barcelona
Sergei Tabachnikov, Pennsylvania State University
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Hardback
9781009320719
Hardback
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.
- Features the research carried out during the special program on Hamiltonian Systems at MSRI during Fall 2018
- Written by leading experts in the field
- Reflects the broad interdisciplinary nature of Hamiltonian systems
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9781009320702
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Table of Contents
- 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.
