Darboux' theorem for Hamiltonian differential operators

Peter J. Olver

Research output: Contribution to journalArticlepeer-review

30 Scopus citations


It is proved that any one-dimensional, first order Hamiltonian differential operator can be put into constant coefficient form by a suitable change of variables. Consequently, there exist canonical variables for any such Hamiltonian operator. In the course of the proof, a complete characterization of all first order Hamiltonian differential operators, as well as the general formula for the behavior of a Hamiltonian operator under a change of variables involving both the independent and the dependent variables are found.

Original languageEnglish (US)
Pages (from-to)10-33
Number of pages24
JournalJournal of Differential Equations
Issue number1
StatePublished - Jan 1988

Bibliographical note

Funding Information:
’ Research was supported in part by NSF Grant MCS 86-02004 and NATO Research Grant RG 86/0055.


Dive into the research topics of 'Darboux' theorem for Hamiltonian differential operators'. Together they form a unique fingerprint.

Cite this