Fractal properties of critical invariant curves

Brian R. Hunt, Konstantin M. Khanin, Yakov G. Sinai, James A. Yorke

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


We examine the dimension of the invariant measure for some singular circle homeomorphisms for a variety of rotation numbers, through both the thermodynamic formalism and numerical computation. The maps we consider include those induced by the action of the standard map on an invariant curve at the critical parameter value beyond which the curve is destroyed. Our results indicate that the dimension is universal for a given type of singularity and rotation number, and that among all rotation numbers, the golden mean produces the largest dimension.

Original languageEnglish (US)
Pages (from-to)261-276
Number of pages16
JournalJournal of Statistical Physics
Issue number1-2
StatePublished - Oct 1996

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


  • Circle homeomorphism
  • Critical curve
  • Fractal dimension
  • Invariant measure
  • Renormalization
  • Rotation number
  • Thermodynamic formalism
  • Twist map


Dive into the research topics of 'Fractal properties of critical invariant curves'. Together they form a unique fingerprint.

Cite this