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In this talk, I will give a survey of results related to the problem of computing Hausdorff dimension of various dynamically defined sets, such as singular vectors. The aim is to try to describe the l...
We consider the evolution of a connected set in Euclidean space carried by a periodic incompressible stochastic ow. While for almost every realization of the random ow at time t most of the part...
The famous ergodic hypothesis suggests that for a typical Hamiltonian on a typical energy surface nearly all trajectories are dense. KAM theory disproves it.Ehrenfest (The Conceptual Foundations of th...
We show that for the Sitnikov example and for the restricted planar circular 3–body problem the set of oscillatory motions often has maximal Hausdorff dimension. Also, we construct Newhouse domains fo...
The measure of the full dimension for a general Sierpi\'{n}ski carpet is studied. In the first part of this study, we give a criterion for the measure of the full Hausdorff dimension of a Sierpi\'{n}s...
The conformal loop ensemble CLE_kappa is the canonical conformally invariant probability measure on non-crossing loops in a proper simply connected domain in the complex plane. The parameter kappa var...
Fine regularity of stochastic processes is usually measured in a local way by local H\"older exponents and in a global way by fractal dimensions. Following a previous work of Adler, we connect these t...
Given a finitely generated semigroup S of the (normed) set of linear maps of a vector space V into itself, we find sufficient conditions for the exponential growth of the number N(k) of elements of th...
The main result of this paper is to show that if N is a normal subgroup of a Kleinian group G such that G/N contains a coset which is represented by some loxodromic element, then the Hausdorff dimensi...
Cutsets of series form an important class of fractal sets. In this paper, the author obtains the Hausdoff dimension of outset of complex valued Rademacher serise.

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