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

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

2011-11-10

arxiv.org/abs/1111.2419v1

Nonlinearity 24 (2011), 2563-2567

Mathematics

Dynamical Systems

Scientific paper

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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