Dynamics of compact quantum metric spaces

Jens Kaad*, David Kyed*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review


We provide a detailed study of actions of the integers on compact quantum metric spaces, which includes general criteria ensuring that the associated crossed product algebra is again a compact quantum metric space in a natural way. Moreover, we provide a flexible set of assumptions ensuring that a continuous family of-Automorphisms of a compact quantum metric space yields a field of crossed product algebras which varies continuously in Rieffel's quantum Gromov-Hausdorff distance. Finally, we show how our results apply to continuous families of Lip-isometric actions on compact quantum metric spaces and to families of diffeomorphisms of compact Riemannian manifolds which vary continuously in the Whitney-Topology.

Original languageEnglish
JournalErgodic Theory and Dynamical Systems
Issue number7
Pages (from-to)2069-2109
Publication statusPublished - Jul 2021


  • 2020 Mathematics Subject Classification
  • 46L05
  • 46L89
  • 47L65
  • dynamics of Riemannian manifolds
  • quantum metric spaces
  • crossed products


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