Hofer distance on Lagrangian links inside the disc

TL;DR

This paper demonstrates that the Hofer distance can be unbounded for Hamiltonian isotopies of specific circle unions inside a disc, using a combination of existing results and standard arguments.

Contribution

It establishes the unboundedness of the Hofer distance for certain Lagrangian links inside the disc, extending understanding of Hamiltonian dynamics.

Findings

Hofer distance is unbounded for certain unions of circles inside the disc.

The proof combines Morabito's result with Khanevsky's standard argument.

The work advances the study of Lagrangian links and Hamiltonian isotopies.

Abstract

We show that the set of Hamiltonian isotopies of certain unions of circles inside the disc is unbounded for the Hofer distance. The proof relies on a result by Francesco Morabito together with a standard argument of Michael Khanevsky.