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We define a Hofer-type norm for the Hamiltonian map on regular Poissonmanifold and prove that it is nondegenerate. We show that the L1,∞-norm and the L∞-normcoincide for the Hamiltonian map on closed regular Poisson manifold and give some sufficientconditions for a Hamiltonian path to be a geodesic. The norm between the Hamiltonian mapand the induced Hamiltonian map on the quotient of Poisson manifold (M,{·,·}) by a compact Lie group Hamiltonian action is also compared

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