Book contents
- Frontmatter
- Contents
- Denjoy subsystems and horseshoes
- Impact Hamiltonian systems and polygonal billiards
- Some remarks on the classical KAM theorem, following Pöschel
- 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
- References
Hamiltonian ODE, homogenization, and symplectic topology
Published online by Cambridge University Press: 10 May 2024
Book contents
- Frontmatter
- Contents
- Denjoy subsystems and horseshoes
- Impact Hamiltonian systems and polygonal billiards
- Some remarks on the classical KAM theorem, following Pöschel
- 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
- References
Summary
This article is based on a course the author gave in the Fall of 2018 at UC Berkeley, in connection with the MSRI program Hamiltonian systems, from topology to applications through analysis. In this article we explore the connection between the Hamiltonian ODEs and Hamilton–Jacobi PDEs, and give an overview of some of the existing techniques for the question of homogenization. We also discuss stochastic formulations of several classical problems in symplectic geometry.
Keywords
- Type
- Chapter
- Information
- Hamiltonian SystemsDynamics, Analysis, Applications, pp. 297 - 367Publisher: Cambridge University PressPrint publication year: 2024
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