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Hamiltonian ODE, homogenization, and symplectic topology

Published online by Cambridge University Press:  10 May 2024

Albert Fathi
Affiliation:
Georgia Institute of Technology
Philip J. Morrison
Affiliation:
University of Texas, Austin
Tere M-Seara
Affiliation:
Universitat Politècnica de Catalunya, Barcelona
Sergei Tabachnikov
Affiliation:
Pennsylvania State University
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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.

Type
Chapter
Information
Hamiltonian Systems
Dynamics, Analysis, Applications
, pp. 297 - 367
Publisher: Cambridge University Press
Print publication year: 2024

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