Hofer's geometry and Floer theory under the quantum limit

TL;DR

This paper explores the relationship between Hofer's geometry and Floer theory to understand the properties of short Hamiltonian paths and their periodic orbits.

Contribution

It introduces a novel approach connecting Floer theory with Hofer's geometry to analyze length minimizing properties of Hamiltonian paths.

Findings

Short Hamiltonian paths have specific periodic orbit characteristics.

Floer theory provides new insights into Hofer length minimization.

The study establishes links between geometric length and dynamical properties.

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.