Hausdorff dimension of limit sets for parabolic ifs with overlaps

K. Simon, B. Solomyak, M. Urbański

Research output: Contribution to journalArticle

21 Citations (Scopus)

Abstract

We study parabolic iterated function systems with overlaps on the real line. We show that if a d-parameter family of such systems satisfies a transversality condition, then for almost every parameter value the Hausdorff dimension of the limit set is the minimum of 1 and the least zero of the pressure function. Moreover, the local dimension of the exceptional set of parameters is estimated. If the least zero is greater than 1, then the limit set (typically) has positive Lebesgue measure. These results are applied to some specific families including those arising from a class of continued fractions.

Original languageEnglish
Pages (from-to)441-478
Number of pages38
JournalPacific Journal of Mathematics
Volume201
Issue number2
DOIs
Publication statusPublished - Dec 2001

ASJC Scopus subject areas

  • Mathematics(all)

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