Stability of iterated function systems on the circle

Tomasz Szarek , Anna Zdunik


We prove that any Iterated Function System of circle homeomorphisms with at least one of them having dense orbit, is asymptotically stable. The corresponding Perron–Frobenius operator is shown to satisfy the e‐property, that is, for any continuous function its iterates are equicontinuous. The Strong Law of Large Numbers for trajectories starting from an arbitrary point for such function systems is also proved.
Author Tomasz Szarek IM
Tomasz Szarek,,
- Institute of Mathematics
, Anna Zdunik
Anna Zdunik,,
Journal seriesBulletin of the London Mathematical Society, ISSN 0024-6093
Issue year2016
Publication size in sheets0.65
Languageen angielski
Score (nominal)30
ScoreMinisterial score = 30.0, 20-12-2017, ArticleFromJournal
Ministerial score (2013-2016) = 30.0, 20-12-2017, ArticleFromJournal
Publication indicators WoS Impact Factor: 2016 = 0.707 (2) - 2016=0.753 (5)
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* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.