Action minimizing properties and distances on the group of Hamiltonian diffeomorphisms
Symplectic Geometry
2014-11-11 v2 Dynamical Systems
Abstract
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 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}.
Keywords
Cite
@article{arxiv.1002.3915,
title = {Action minimizing properties and distances on the group of Hamiltonian diffeomorphisms},
author = {Alfonso Sorrentino and Claude Viterbo},
journal= {arXiv preprint arXiv:1002.3915},
year = {2014}
}
Comments
21pp, accepted for publication in Geometry & Topology