One-parameter Families of Circle Diffeomorphisms with Strictly Monotone Rotation Number
نویسنده
چکیده
We show that if f : S1 × S1 → S1 × S1 is C2, with f(x, t) = (ft(x), t), and the rotation number of ft is equal to t for all t ∈ S1, then f is topologically conjugate to the linear Dehn twist of the torus ( 1 1 0 1 ) . We prove a differentiability result where the assumption that the rotation number of ft is t is weakened to say that the rotation number is strictly monotone in t.
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