Canonical equivalence of integrable systems, their associated (semi)- groups, and moment systems
type: Item
instance of: scholarly article
title: Canonical equivalence of integrable systems, their associated (semi)- groups, and moment systems
zbMATH Open document ID: 0614.70015
DOI: 10.1016/0022-247X(86)90011-9
published in: Journal of Mathematical Analysis and Applications
publication date: 1986-01-01T00:00:00Z
review text: The author considers Hamiltonian systems on \({\mathbb{R}}^{2n}\). A system is defined to be integrable when the Hamiltonian is a function of the momenta only. It is shown by the construction of generating functions that any two integrable systems are equivalent. For the corresponding quantum system, a unitary transformation is constructed with maps the Hilbert spaces associated to each system onto each other. Moment systems for a Hamiltonian system are defined following \textit{P. Feinsilver} [Special functions, probability semigroups, and Hamiltonian flows (1978; Zbl 0394.33002)]. These moment systems and related semigroups introduced by Feinsilver can again be related in a canonical fashion.
Mathematics Subject Classification ID: 70H15
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 70H20
Mathematics Subject Classification ID: 81Q99
zbMATH DE Number: 3995113
zbMATH Keywords: Hamiltonian systems
zbMATH Keywords: generating functions
zbMATH Keywords: integrable systems
zbMATH Keywords: quantum system
zbMATH Keywords: unitary transformation
zbMATH Keywords: Hilbert spaces
zbMATH Keywords: Moment systems
zbMATH Keywords: semigroups
author: Henryk Gzyl
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3995113