Non-uniqueness of ergodic measures with full Hausdorff dimension on a   Gatzouras-Lalley carpet
  In this note, we show that on certain Gatzouras-Lalley carpet, there exist more than one ergodic measures with full Hausdorff dimension. This gives a negative answer to a conjecture of Gatzouras and Peres. 
Julien Barral and De-Jun Feng
math.DS math.CA