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

[摘要] We define a Hofer-type norm for the Hamiltonian map on regular Poissonmanifold and prove that it is nondegenerate. We show that theL1,∞-norm and theL∞-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.

[学科分类] 应用数学