Piecewise linear circle maps and conjugation to rigid rational rotations

Paul Glendinning, Siyuan Ma, James Montaldi

Criteria for piecewise linear circle homeomorphisms to be conjugate to a rigid rotation, $x\to x+\ddot{I}‰(\mathrm{mod}1)$, with rational rotation number $\ddot{I}‰$ are given. The consequences o…