Contracting on average random IFS with repelling fixed point

Ai Hua Fan, Károly Simon, Hajnal R. Tóth

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5 Citations (Scopus)


We consider random iterated function systems which consist of strictly increasing and (not necessarily strictly) convex functions on a compact interval or on a half line. We assume that the system is contracting on average in a sense which is wide enough to permit the existence of a common fixpoint at which some functions of the system are expanding and perhaps none of them are contracting (see Fig. 1). We prove that the Hausdorff dimension of any of the possibly uncountably many invariant measures is smaller than or equal to the accumulated entropy divided by the Liapunov exponent.

Original languageEnglish
Pages (from-to)169-193
Number of pages25
JournalJournal of Statistical Physics
Issue number1
Publication statusPublished - Jan 1 2006



  • Contracting on average
  • Hausdorff dimension

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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