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

TL;DR

This paper identifies conditions under which certain non-conformal carpets have a unique ergodic measure of full dimension, especially near Sierpinski carpets, contributing to the understanding of measure uniqueness in complex fractals.

Contribution

It establishes a subclass of Lalley-Gatzouras carpets with an open set where full dimension measures are unique, extending results to carpets close to Sierpinski carpets.

Findings

Existence of a subclass with unique ergodic measure of full dimension.

Stability of measure uniqueness near Sierpinski carpets.

Characterization of non-conformal carpets with measure uniqueness.

Abstract

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.