On the autonomous norm on the group of Hamiltonian diffeomorphisms of the torus-Reference-Cited by-同舟云学术

On the autonomous norm on the group of Hamiltonian diffeomorphisms of the torus

Published:2017-11-29 Issue:02 Volume:20 Page:1750042
ISSN:0219-1997
Container-title:Communications in Contemporary Mathematics
language:en
Short-container-title:Commun. Contemp. Math.

Author:

Brandenbursky Michael¹,Kędra Jarek²³,Shelukhin Egor⁴⁵

Affiliation:

1. Department of Mathematics, Ben Gurion University, Beer Sheva 84105, Israel

2. Institute of Mathematics, University of Aberdeen, AB243UE Aberdeen, Scotland

3. Institute of Mathematics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland

4. Department of Mathematics and Statistics, University of Montreal, Montreal QC H3C 3J7, Canada

5. Institute for Advanced Study, 1 Einstein Drive, Princeton NJ 08540, USA

Abstract

We prove that the autonomous norm on the group of Hamiltonian diffeomorphisms of the two-dimensional torus is unbounded. We provide examples of Hamiltonian diffeomorphisms with arbitrarily large autonomous norm. For the proofs we construct explicit quasimorphisms on [Formula: see text] some of them are [Formula: see text]-continuous and vanish on all autonomous diffeomorphisms, and some of them are Calabi.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219199717500420

Reference20 articles.

1. On the palindromic and primitive widths of a free group

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5. Advanced Studies in Pure Mathematics;Burago D.,2008

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