Abstract
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 language | English |
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Pages (from-to) | 23-41 |
Journal | Pacific Journal of Mathematics |
Volume | 184 |
Issue number | 1 |
DOIs | |
Publication status | Published - 1 Jan 1998 |