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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 879196, 9 pages
http://dx.doi.org/10.1155/2014/879196
Research Article

A Hofer-Type Norm of Hamiltonian Maps on Regular Poisson Manifold

1College of Science, Henan University of Technology, Zhengzhou 450001, China
2School of Mathematical Sciences, Nankai University, Tianjin 300071, China

Received 17 November 2013; Accepted 8 February 2014; Published 27 March 2014

Academic Editor: Jin L. Kuang

Copyright © 2014 Dawei Sun and Zhenxing Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 -norm and the -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 by a compact Lie group Hamiltonian action is also compared.