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.
"A Hofer-Type Norm of Hamiltonian Maps on Regular Poisson Manifold." J. Appl. Math. 2014 1 - 9, 2014. https://doi.org/10.1155/2014/879196