Properties of infinite dimensional Hamiltonian systems
type: Item
instance of: scholarly article
title: Properties of infinite dimensional Hamiltonian systems
zbMATH Open document ID: 0301.58016
author: Paul R. Chernoff
author: J. E. Marsden
published in: Lecture Notes in Mathematics
publication date: 1974-01-01T00:00:00Z
review text: To appreciate these notes the reader should be well grounded in the theory of finite-dimensional Hamiltonian and Lagrangian systems, symplectic manifolds, and Lie groups. The purpose of these notes is to generalize all of this material to infinite dimensions, where the difference between the bounded und unbounded linear operators becomes important. In this regard the authors lean heavily on such tools as Stone's theorem and the Hille-Yosida theorem. Many examples from quantum mechanics and symmetric hyperbolic systems of partial differential equations are given by the authors to show the applicability of this approach. Contents: Ch. 1: Symplectic structures and Hamiltonian systems. Ch. 2: Linear Hamiltonian systems. Ch. 3: Some general properties of nonlinear semigroups. Ch. 4: Hamiltonian systems. Ch. 5: Lagrangian systems. Ch. 6: Symmetry groups and conservation laws.
Mathematics Subject Classification ID: 37K05
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 37-02
Mathematics Subject Classification ID: 47D03
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 70H03
Mathematics Subject Classification ID: 70H05
Mathematics Subject Classification ID: 70H15
zbMATH DE Number: 3471338
zbMATH Keywords: infinite dimensional Hamiltonian systems
zbMATH Keywords: Lagrangian systems
zbMATH Keywords: symplectic structures
zbMATH Keywords: nonlinear semigroups
zbMATH Keywords: symmetry groups
zbMATH Keywords: conservation laws
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bfb0073665
OpenAlex ID: W1493997298
DOI: 10.1007/BFB0073665
description: scientific article; zbMATH DE number 3471338