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Non-uniqueness of ergodic measures with full Hausdorff dimension on a Gatzouras-Lalley carpet

Published 10 Nov 2011 in math.DS and math.CA | (1111.2419v1)

Abstract: 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.

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