Date
2010
Lien vers un document non conservé dans cette base
http://hal.archives-ouvertes.fr/hal-00458323/fr/
Indexation documentaire
Analyse
Subject
Asymptotic Hofer distance; action-minimizing measure; symplectic homogenization; Mather's beta function; Mather's minimal average action; Viterbo distance; Mather theory; Aubry–Mather theory
Nom de la revue
Geometry and Topology
Volume
14
Numéro
4
Date de publication
2010
Pages article
2383–2403
Nom de l'éditeur
Mathematical Sciences Publishers
Auteur
Viterbo, Claude
Sorrentino, Alfonso
Type
Article accepté pour publication ou publié
Résumé en anglais
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}.
