Mathematics – Dynamical Systems
Scientific paper
1991-04-27
Mathematics
Dynamical Systems
Scientific paper
We estimate harmonic scalings in the parameter space of a one-parameter
family of critical circle maps. These estimates lead to the conclusion that
the Hausdorff dimension of the complement of the frequency-locking set is less
than $1$ but not less than $1/3$. Moreover, the rotation number is a
H\"{o}lder continuous function of the parameter.
Graczyk Jacek
Świątek Grzegorz
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