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Scalings in circle maps. I. (English) Zbl 0723.58026
The authors consider a “flat spot” circle map with irrational rotation number. They define scalings associated with the closest returns of the orbit of the critical point. Under a certain condition that these scalings go to zero, a proof is given of the property that the derivative of long iterates of the critical value can be expressed in the scalings. The authors study also the asymptotic behavior of the derivatives and the scalings.

MSC:
37B99 Topological dynamics
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