Dimensional characteristics of invariant measures for circle diffeomorphisms

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


We consider pointwise, box, and Hausdorff dimensions of invariant measures for circle diffeomorphisms. We discuss the cases of rational, Diophantine, and Liouville rotation numbers. Our main result is that for any Liouville number there exists a C circle diffeomorphism with rotation number such that the pointwise and box dimensions of its unique invariant measure do not exist. Moreover, the lower pointwise and lower box dimensions can equal any value 0≥β≥1.

Original languageEnglish (US)
Pages (from-to)1979-1992
Number of pages14
JournalErgodic Theory and Dynamical Systems
Issue number6
StatePublished - Dec 2009

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics


Dive into the research topics of 'Dimensional characteristics of invariant measures for circle diffeomorphisms'. Together they form a unique fingerprint.

Cite this