1 citations · 1 across the 6 of their papers we have counts for
8 papers
Lipschitz continuity of the Hausdorff dimension of self-affine sponges at Sierpinski sponges
Nuno Luzia
The Hausdorff dimension of general Sierpinski carpets, [4] and [20], and the generalization on Lalley-Gatzouras carpets, [10], are today well known results, the formulas being obta…
On the uniqueness of an ergodic measure of full dimension for non-conformal repellers
Nuno Luzia
We give a subclass L of Non-linear Lalley-Gatzouras carpets and an open set U in L such that any carpet in U has a unique ergodic measure of full dimension. In particular, any Lall…
Other trigonometric proofs of Pythagoras theorem
Nuno Luzia
Only very recently a trigonometric proof of the Pythagoras theorem was given by Zimba \cite{1}, many authors thought this was not possible. In this note we give other trigonometric…
Quantitative recurrence results for random walks
Nuno Luzia
First, we prove a \emph{local almost sure central limit theorem} for lattice random walks in the plane. The corresponding version for random walks in the line was considered by the…
A Borel-Cantelli lemma and its applications
Nuno Luzia
We give a version of the Borel-Cantelli lemma. As an application, we prove an almost sure local central limit theorem. As another application, we prove a dynamical Borel-Cantelli l…
Hausdorff dimension of certain random self--affine fractals
Nuno Luzia
In this work we are interested in the self--affine fractals studied by Gatzouras and Lalley and by the author which generalize the famous general Sierpinski carpets studied by Bedf…
The Hausdorff dimension of self-affine Sierpinski sponges
Nuno Luzia
We compute the Hausdorff dimension of limit sets generated by 3-dimensional self-affine mappings with diagonal matrices of the form A_{ijk}=Diag(a_{ijk}, b_{ij}, c_{i}), where 0<a_…
Measure of full dimension for some nonconformal repellers
Nuno Luzia
We prove the existence of an ergodic measure with full Hausdorff dimension for a class of nonlinear nonconformal skew-product transformations. In order to do so we establish a vari…