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

Michael Brandenbursky; Jarek Kȩdra; Egor Shelukhin

doi:https://doi.org/10.1142/S0219199717500420

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

Michael Brandenbursky, Jarek Kȩdra, Egor Shelukhin

Department of Mathematics

Ben-Gurion University of the Negev

Research output: Contribution to journal › Article › peer-review

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 Ham(T2), some of them are C0-continuous and vanish on all autonomous diffeomorphisms, and some of them are Calabi.

Original language	American English
Article number	1750042
Journal	Communications in Contemporary Mathematics
Volume	20
Issue number	2
DOIs	https://doi.org/10.1142/S0219199717500420
State	Published - 1 Mar 2018

Keywords

Hamiltonian diffeomorphisms
autonomous norm
braid groups
quasi-morphisms

All Science Journal Classification (ASJC) codes

Applied Mathematics
General Mathematics

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https://doi.org/10.1142/S0219199717500420

Cite this

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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 Ham(T2), some of them are C0-continuous and vanish on all autonomous diffeomorphisms, and some of them are Calabi.",

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AB - 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 Ham(T2), some of them are C0-continuous and vanish on all autonomous diffeomorphisms, and some of them are Calabi.

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KW - braid groups

KW - quasi-morphisms

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

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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