A Hofer-Type Norm of Hamiltonian Maps on Regular Poisson Manifold. (27th March 2014) - Sun, Dawei; Zhang, Zhenxing
Abstract : 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.