We obtain bounds for the generalized q-dimensions of measures supported by self-affine sets that ate valid for 'almost all' families of affine mappings. Exact values are established for self-affine measures and for Gibbs measures when 1 < q less than or equal to 2. These q-dimensions may exhibit phase transitions as q varies.</p
An affine iterated function system is a finite collection of affine invertible contractions and the...
We study the upper regularity dimension which describes the extremal local scaling behaviour of a me...
We show the existence of the local dimension of an invariant probability measure on an infinitely ge...
We obtain bounds for the generalized q-dimensions of measures supported by self-affine sets that ate...
We study the Lq-dimensions of self-affine measures and the Käenmäki measure on a class of self-affin...
The authors were financially supported by an LMS Scheme 4 Research in Pairs grant. The second author...
Abstract: We study L q -spectra of planar self-affine measures generated by diagonal matrices. We in...
We study the dimension theory of a class of planar self-affine multifractal measures. These measures...
Under mild conditions we show that the affinity dimension of a planar self-affine set is equal to t...
We study equilibrium measures (Käenmäki measures) supported on self-affine sets generated by a finit...
We derive upper and lower bounds for the Assouad and lower dimensions of self-affine measures in ℝd ...
In this paper, we solve the long standing open problem on exact dimensionality of self-affine measu...
We study the dimension theory of a class of planar self-affine multifractal measures. These mea-sure...
We investigate a formula of K. Falconer which describes the typical value of the generalised R´enyi ...
summary:In this paper, we first prove that the self-affine sets depend continuously on the expanding...
An affine iterated function system is a finite collection of affine invertible contractions and the...
We study the upper regularity dimension which describes the extremal local scaling behaviour of a me...
We show the existence of the local dimension of an invariant probability measure on an infinitely ge...
We obtain bounds for the generalized q-dimensions of measures supported by self-affine sets that ate...
We study the Lq-dimensions of self-affine measures and the Käenmäki measure on a class of self-affin...
The authors were financially supported by an LMS Scheme 4 Research in Pairs grant. The second author...
Abstract: We study L q -spectra of planar self-affine measures generated by diagonal matrices. We in...
We study the dimension theory of a class of planar self-affine multifractal measures. These measures...
Under mild conditions we show that the affinity dimension of a planar self-affine set is equal to t...
We study equilibrium measures (Käenmäki measures) supported on self-affine sets generated by a finit...
We derive upper and lower bounds for the Assouad and lower dimensions of self-affine measures in ℝd ...
In this paper, we solve the long standing open problem on exact dimensionality of self-affine measu...
We study the dimension theory of a class of planar self-affine multifractal measures. These mea-sure...
We investigate a formula of K. Falconer which describes the typical value of the generalised R´enyi ...
summary:In this paper, we first prove that the self-affine sets depend continuously on the expanding...
An affine iterated function system is a finite collection of affine invertible contractions and the...
We study the upper regularity dimension which describes the extremal local scaling behaviour of a me...
We show the existence of the local dimension of an invariant probability measure on an infinitely ge...
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