A Hofer-type norm of Hamiltonian maps on regular Poisson manifold (Q1714801)

Summary: 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 \((N,\{\cdot,\cdot\})\) by a compact Lie group Hamiltonian action is also compared.