The dimension spectrum of some dynamical systems

P. Collet, Joel Lebowitz, A. Porzio

Research output: Contribution to journalArticle

172 Scopus citations


We analyze the dimension spectrum previously introduced and measured experimentally by Jensen, Kadanoff, and Libchaber. Using large-deviation theory, we prove, for some invariant measures of expanding Markov maps, that the Hausdorff dimension f(α) of the set on which the measure has a singularity α is a well-defined, concave, and regular function. In particular, we show that this is the case for the accumulation of period doubling and critical mappings of the circle with golden rotation number. We also show in these particular cases that the function f is universal.

Original languageEnglish (US)
Pages (from-to)609-644
Number of pages36
JournalJournal of Statistical Physics
Issue number5-6
StatePublished - Jan 1 1987

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


  • Hausdorff dimension spectrum
  • critical circle map
  • partition function
  • period doubling
  • universality

Fingerprint Dive into the research topics of 'The dimension spectrum of some dynamical systems'. Together they form a unique fingerprint.

  • Cite this