Dimensional characteristics of invariant measures for circle diffeomorphisms

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

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
Volume29
Issue number6
DOIs
StatePublished - Dec 1 2009

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Box Dimension
Liouville's number
Diffeomorphisms
Invariant Measure
Circle
Rotation number
Diffeomorphism
Hausdorff Dimension

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

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abstract = "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.",
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Dimensional characteristics of invariant measures for circle diffeomorphisms. / Sadovskaya, Victoria.

In: Ergodic Theory and Dynamical Systems, Vol. 29, No. 6, 01.12.2009, p. 1979-1992.

Research output: Contribution to journalArticle

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