Critical circle maps near bifurcation
Dynamical Systems
2016-09-06 v1
Abstract
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 but not less than . Moreover, the rotation number is a H\"{o}lder continuous function of the parameter.
Cite
@article{arxiv.math/9201283,
title = {Critical circle maps near bifurcation},
author = {Jacek Graczyk and Grzegorz Swiatek},
journal= {arXiv preprint arXiv:math/9201283},
year = {2016}
}