Abstract
We prove that for the generic C 1 arc of circle diffeomorphisms, t ↦ f t , the rotation number t ↦ ρ( f t ) is a piecewise monotone function of t. A proof of this was attempted by Brunovsky in 1970. We also show that our methods cannot hope to answer the corresponding question for C r arcs of circle diffeomorphisms when r is ≥ 2.
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