A Hofer-Type Norm of Hamiltonian Maps on Regular Poisson Manifold. (27th March 2014)

• Record Type: Journal Article
• Authors: Sun, Dawei; Zhang, Zhenxing
• Other Names: Kuang Jin L. Academic Editor.
• Is Part Of: Journal of applied mathematics. Volume 2014(2014)
• Publication Date: 2014-03-27
• Subjects: Mathematics -- Periodicals; 519.05
• DOI: 10.1155/2014/879196
• Languages: English
• ISSNs: 1110-757X

Abstract

Abstract : We define a Hofer-type norm for the Hamiltonian map on regular Poisson manifold and prove that it is nondegenerate. We show that the L 1, ∞ -norm and the L ∞ -norm coincide for the Hamiltonian map on closed regular Poisson manifold and give some sufficient conditions for a Hamiltonian path to be a geodesic. The norm between the Hamiltonian map and the induced Hamiltonian map on the quotient of Poisson manifold ( M, { ·, · } ) by a compact Lie group Hamiltonian action is also compared.