5 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…
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…
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…