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

Michael Brandenbursky, Jarek Kȩdra, Egor Shelukhin

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

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
JournalCommunications in Contemporary Mathematics
Volume20
Issue number2
DOIs
StatePublished - 1 Mar 2018

Keywords

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

ASJC Scopus subject areas

  • Mathematics (all)
  • Applied Mathematics

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