71 research outputs found
Singularity of projections of 2-dimensional measures invariant under the geodesic flow
We show that on any compact Riemann surface with variable negative curvature
there exists a measure which is invariant and ergodic under the geodesic flow
and whose projection to the base manifold is 2-dimensional and singular with
respect to the 2-dimensional Lebesgue measure.Comment: 12 page
Hausdorff dimension of affine random covering sets in torus
We calculate the almost sure Hausdorff dimension of the random covering set
in -dimensional torus ,
where the sets are parallelepipeds, or more generally,
linear images of a set with nonempty interior, and are
independent and uniformly distributed random points. The dimension formula,
derived from the singular values of the linear mappings, holds provided that
the sequences of the singular values are decreasing.Comment: 16 pages, 1 figur
Dimensions of random affine code tree fractals
We calculate the almost sure Hausdorff dimension for a general class of
random affine planar code tree fractals. The set of probability measures
describing the randomness includes natural measures in random -variable and
homogeneous Markov constructions.Comment: 22 page
Hitting probabilities of random covering sets in tori and metric spaces
We provide sharp lower and upper bounds for the Hausdorff dimension of the intersection of a typical random covering set with a fixed analytic set both in Ahlfors regular metric spaces and in the -dimensional torus. In metric spaces, we consider covering sets generated by balls and, in the torus, we deal with general analytic generating sets
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