32 citations · 76 across the 13 of their papers we have counts for
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Hyperbolicity is dense in the real quadratic family
Grzegorz Swiatek
It is shown that for non-hyperbolic real quadratic polynomials topological and quasisymmetric conjugacy classes are the same. By quasiconformal rigidity, each class has only one re…
Singular measures in circle dynamics
Jacek Graczyk, Grzegorz Swiatek
Critical circle homeomorphisms have an invariant measure totally singular with respect to the Lebesgue measure. We prove that singularities of the invariant measure are of Holder t…
Scalings in circle maps III
Jacek Graczyk, Grzegorz Swiatek, Folkert Tangerman +1
Circle maps with a flat spot are studied which are differentiable, even on the boundary of the flat spot. Estimates on the Lebesgue measure and the Hausdorff dimension of the non-w…
Quasisymmetric conjugacies between unimodal maps
Michael Jakobson, Grzegorz Swiatek
It is shown that some topological equivalency classes of S-unimodal maps are equal to quasisymmetric conjugacy classes. This includes some infinitely renormalizable polynomials of…
Critical circle maps near bifurcation
Jacek Graczyk, Grzegorz Swiatek
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 c…
One-dimensional maps and Poincaré metric
Grzegorz Swiatek
Invertible compositions of one-dimensional maps are studied which are assumed to include maps with non-positive Schwarzian derivative and others whose sum of distortions is bounded…