Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1098.37540
Fuchssteiner, Benno
The Lie algebra structure of degenerate Hamiltonian and bi-Hamiltonian systems. (English)
[J] Prog. Theor. Phys. 68, No. 4, 1082-1104 (1982). ISSN 0033-068X

Summary: A generalization of Noether's theorem is obtained via an extension of the well-known Poisson bracket formalism. It is shown that degenerate closed forms yield Lie algebra homomorphisms between vector fields and covector fields. A similar result holds for operators working in the opposite way. Application of these Lie algebra homomorphisms to a dynamical system having two (degenerate) Hamiltonian formulations yields a self-map in the space of infinitesimal generators of one-parameter symmetry groups of this system. These Hamiltonian formulations are not assumed to constitute a Hamiltonian pair (in the sense of Gelfand-Dorfman). Thus infinite-dimensional symmetry groups for a wider class of equations can be constructed. Several new equations are shown to admit infinite-dimensional symmetry groups.

MSC 2000:: *37K30 Relations with algebraic structures

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]