A translation of "The Geometry of the Group of Symplectic Diffeomorphisms"

TL;DR

This work introduces Hofer's metric on Hamiltonian diffeomorphisms, exploring geometric properties like diameter and geodesics, and applying these insights to dynamics and ergodic theory.

Contribution

It provides a comprehensive introduction to Hofer's metric, including new results on geometric properties and their implications for dynamical systems.

Findings

Hofer's metric has finite diameter in certain cases

Existence of geodesics in the Hamiltonian diffeomorphism group

Growth rates of one-parameter subgroups analyzed

Abstract

This book offers an introduction to Hofer's metric on the group of Hamiltonian diffeomorphisms. It presents results on the diameter, geodesics, and the growth of one-parameter subgroups, along with applications to dynamics and ergodic theory.