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

Michael Brandenbursky, Jarek Kedra, Egor Shelukhin

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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.
Original languageEnglish
Article number1750042
Number of pages27
JournalCommunications in Contemporary Mathematics
Volume20
Issue number2
Early online date24 May 2017
DOIs
Publication statusPublished - 2 Mar 2018

Keywords

  • braid groups
  • autonomous norm
  • quasi-morphisms
  • Hamiltonian diffeomorphisms

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