"Arising from the MSRI program on Hamiltonian Systems during Fall 2018, this carefully edited volume contains research papers, surveys, and lecture notes spanning a broad range of topics. It will be a standard reference and introduction to the subject for researchers and graduate students working in dynamical systems"--
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.
Arising from the MSRI program on Hamiltonian Systems during Fall 2018, this carefully edited volume contains research papers, surveys, and lecture notes spanning a broad range of topics. It will be a standard reference and introduction to the subject for researchers and graduate students working in dynamical systems.
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A selection of results, spanning a broad spectrum of disciplines, from the MSRI program on Hamiltonian Systems during Fall 2018.
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 HamiltonJacobi 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.
Albert Fathi is Professor of the Practice in the School of Mathematics at Georgia Institute of Technology. Philip J. Morrison is TAERF Professor of Physics at the University of Texas. Tere M-Seara is a professor at Universitat Politècnica de Catalunya, Barcelona, and a member of the Centre de Recerca Matemàtica. Sergei Tabachnikov is Professor of Mathematics at Pennsylvania State University.
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