Length minimizing paths in the Hamiltonian diffeomorphism group
نویسندگان
چکیده
منابع مشابه
Hofer–Zehnder capacity and length minimizing Hamiltonian paths
We use the criteria of Lalonde and McDuff to show that a path that is generated by a generic autonomous Hamiltonian is length minimizing with respect to the Hofer norm among all homotopic paths provided that it induces no non-constant closed trajectories in M . This generalizes a result of Hofer for symplectomorphisms of Euclidean space. The proof for general M uses Liu–Tian’s construction of S...
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We use the criteria of Lalonde and McDuff to determine a new class of examples of length minimizing paths in the group Ham(M). For a compact symplectic manifold M of dimension two or four, we show that a path inHam(M), generated by an autonomous Hamiltonian and starting at the identity, which induces no non-constant closed trajectories of points in M , is length minimizing among all homotopic p...
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ژورنال
عنوان ژورنال: Journal of Symplectic Geometry
سال: 2008
ISSN: 1527-5256,1540-2347
DOI: 10.4310/jsg.2008.v6.n2.a3