Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4606516 | Differential Geometry and its Applications | 2008 | 5 Pages |
Abstract
Let (M,ω)(M,ω) be a symplectic manifold and G a compact Lie group that acts on M. Assume that the action of G on M is Hamiltonian. Then a G-equivariant Hamiltonian map on M induces a map on the symplectic quotient of M by G. Consider an autonomous Hamiltonian H with compact support on M , with no non-constant closed trajectory in time less than 1 and time-1 map fHfH. If the map fHfH descends to the symplectic quotient to a map Φ(fH)Φ(fH) and the symplectic manifold M is exact and Ham(M,ω)Ham(M,ω) has no short loops, we prove that the Hofer norm of the induced map Φ(fH)Φ(fH) is bounded above by the Hofer norm of fHfH.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Andrés Pedroza,