Refined measurable rigidity and flexibility for conformal iterated function systems.
Measure-geometric Laplacians for partially atomic measures
Motivated by the fundamental theorem of calculus, and based on the works of W. Feller as well as M. Kac and M. G. Kreĭn, given an atomless Borel probability measure supported on a compact subset of U. Freiberg and M. Zähle introduced a measure-geometric approach to define a first order differential operator and a second order differential operator , with respect to . We generalize this approach to measures of the form , where is non-atomic and is finitely supported. We determine analytic...
Sets of nondifferentiability for conjugacies between expanding interval maps
We study differentiability of topological conjugacies between expanding piecewise interval maps. If these conjugacies are not C¹, then their derivative vanishes Lebesgue almost everywhere. We show that in this case the Hausdorff dimension of the set of points for which the derivative of the conjugacy does not exist lies strictly between zero and one. Moreover, by employing the thermodynamic formalism, we show that this Hausdorff dimension can be determined explicitly in terms of the Lyapunov spectrum....
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