Une condition suffisante de minimalité pour les géodésiques de la métrique de Hofer

Abstract

We give a new sufficient condition for a Hamiltonian H to generate a length minimizing geodesic of the Hofer's metric on the group of Hamiltonian diffeomorphisms on R 2n . This condition is related to the spectra of the linearized maps of the flow { φ H t } generated by H at the fixed points of the flow. In addition we show that if φ 0, φ 1 are two diffeomorphisms linked by such a geodesic, then the Hofer's distance between φ 0 and φ 1 is the same as Viterbo's one. To cite this article: J. Le Crapper, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 359–364.