On the uniqueness of an ergodic measure of full dimension for non-conformal repellers

Nuno Luzia

doi:10.3934/dcds.2017250

Article Contents

2017, Volume 37, Issue 11: 5763-5780. Doi: 10.3934/dcds.2017250

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On the uniqueness of an ergodic measure of full dimension for non-conformal repellers

Nuno Luzia

Universidade Federal do Rio de Janeiro, Instituto de Matemática, Rio de Janeiro, 21941-909, RJ, Brazil

Received: May 31, 2016

Revised: May 31, 2017

Published: October 2017

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Abstract

We give a subclass $\mathcal{L}$ of Non-linear Lalley-Gatzouras carpets and an open set $\mathcal{U}$ in $\mathcal{L}$ such that any carpet in $\mathcal{U}$ 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.

Keywords:

Measure of full dimension,
non-conformal repeller.

Mathematics Subject Classification: Primary: 37D35, 37C45.

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References

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