Badly ordered cycles of circle maps

Lluís Alsedà, Jaume Llibre, Michal Misiurewicz

Research output: Contribution to journalArticleResearchpeer-review

3 Citations (Scopus)


A cycle of a circle map of degree one is badly ordered if it cannot be divided into blocks of consecutive points, such that the blocks are permuted by the map like points of a cycle of a rational rotation. We find the smallest possible rotation intervals that a map with a badly ordered cycle of a given rotation number and period can have. Moreover, we show that if one of those intervals is contained in the interior of the rotation interval of a map then the map has a corresponding badly ordered cycle.
Original languageEnglish
Pages (from-to)23-41
JournalPacific Journal of Mathematics
Issue number1
Publication statusPublished - 1 Jan 1998


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