The autonomous norm on $Ham(\mathbf{R}^{2n})$ is bounded

TL;DR

This paper proves that the autonomous norm on the group of compactly supported Hamiltonian diffeomorphisms of standard Euclidean space is bounded, providing new insights into the structure of this mathematical group.

Contribution

It establishes the boundedness of the autonomous norm on the group of compactly supported Hamiltonian diffeomorphisms of n, a previously unknown property.

Findings

The autonomous norm on the group is bounded.

The result applies to n with standard structure.

This advances understanding of Hamiltonian diffeomorphism groups.

Abstract

We prove that the autonomous norm on the group of compactly supported Hamiltonian diffeomorphisms of the standard $\mathbf{R}^{2n}$ is bounded.