On the uniqueness of an ergodic measure of full dimension for   non-conformal repellers
  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 Lalley-Gatzouras carpet which is close to a non-trivial general Sierpinski carpet has a unique ergodic measure of full dimension. 
Nuno Luzia
math.DS