Fathi A. Hamiltonian Systems. Dynamics, Analysis, Applications 2024

Textbook in PDF format

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
Denjoy subsystems and horseshoes
Impact Hamiltonian systems and polygonal billiards
Some remarks on the classical KAM theorem, following Pösche
Some recent developments in Arnold diffusion
Viscosity solutions of the Hamilton–Jacobi equation on a noncompact manifold
Holonomy and vortex structures in quantum hydrodynamics
Surfaces of locally minimal flux
A symplectic approach to Arnold diffusion problems
Hamiltonian ODE, homogenization, and symplectic topology