Action minimizing properties and distances on the group of Hamiltonian diffeomorphisms

Details Action minimizing properties and distances on the group of Hamiltonian diffeomorphisms Action minimizing properties and distances on the group of Hamiltonian diffeomorphisms

2010-02-20

arxiv.org/abs/1002.3915v2

Mathematics

Symplectic Geometry

21pp, accepted for publication in Geometry & Topology

Scientific paper

In this article we prove that for a smooth fiberwise convex Hamiltonian, the asymptotic Hofer distance from the identity gives a strict upper bound to the value at 0 of Mather's $\beta$ function, thus providing a negative answer to a question asked by K. Siburg in \cite{Siburg1998}. However, we show that equality holds if one considers the asymptotic distance defined in \cite{Viterbo1992}.

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