## Journal of Applied Mathematics

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

#### 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 ${L}^{1,\infty }$-norm and the ${L}^{\infty }$-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.

#### Article information

Source
J. Appl. Math., Volume 2014 (2014), Article ID 879196, 9 pages.

Dates
First available in Project Euclid: 2 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.jam/1425305640

Digital Object Identifier
doi:10.1155/2014/879196

Mathematical Reviews number (MathSciNet)
MR3191140

Zentralblatt MATH identifier
07010786

#### Citation

Sun, Dawei; Zhang, Zhenxing. A Hofer-Type Norm of Hamiltonian Maps on Regular Poisson Manifold. J. Appl. Math. 2014 (2014), Article ID 879196, 9 pages. doi:10.1155/2014/879196. https://projecteuclid.org/euclid.jam/1425305640

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