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Separation conditions on controlled Moran constructions

Antti Käenmäki, Markku Vilppolainen (2008)

Fundamenta Mathematicae

It is well known that the open set condition and the positivity of the t-dimensional Hausdorff measure are equivalent on self-similar sets, where t is the zero of the topological pressure. We prove an analogous result for a class of Moran constructions and we study different kinds of Moran constructions in this respect.

Sets of nondifferentiability for conjugacies between expanding interval maps

Thomas Jordan, Marc Kesseböhmer, Mark Pollicott, Bernd O. Stratmann (2009)

Fundamenta Mathematicae

We study differentiability of topological conjugacies between expanding piecewise C 1 + ϵ 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....

Subadditive Pressure for IFS with Triangular Maps

Balázs Bárány (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

We investigate properties of the zero of the subadditive pressure which is a most important tool to estimate the Hausdorff dimension of the attractor of a non-conformal iterated function system (IFS). Our result is a generalization of the main results of Miao and Falconer [Fractals 15 (2007)] and Manning and Simon [Nonlinearity 20 (2007)].

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