A Hofer-type norm of Hamiltonian maps on regular Poisson manifold

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. © 2014 dawei sun and zhenxing zhang.