2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/139294In this paper, we use Floer theory to study the Hofer length functional for paths of Hamiltonian diffeomorphisms which are sufficiently short. In particular, the length minimizing properties of a short Hamiltonian path are related to the properties and number of its periodic orbits.This is major revision. Section 2 has been completely reworked to correct a gap in the previous version of Proposition 2.5. The main results have been slightly improved, and figures and examples have been added. 29 pagesSymplectic GeometryDifferential Geometry53D40; 37J45text