Hofer's geometry and Floer theory under the quantum limit
arXiv:math/0703064
Abstract
In 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 pages