Hamiltonian Systems: Dynamics, Analysis, Applications

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Albert Fathi (Georgia Institute of Technology) Philip J. Morrison (University of Texas, Austin)

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)

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English

Cambridge University Press
09 May 2024

Differential calculus & equations; Differential & Riemannian geometry; Fluid mechanics; Mathematical physics

Series: Mathematical Sciences Research Institute Publications

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.

Edited by: 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)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions: Height: 234mm, Width: 156mm, Spine: 22mm
Weight: 751g
ISBN: 9781009320719
ISBN 10: 1009320718
Series: Mathematical Sciences Research Institute Publications
Pages: 375
Publication Date: 09 May 2024
Audience: College/higher education , Further / Higher Education
Format: Hardback
Publisher's Status: Active

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.

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.