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arXiv · 1701.08575

On natural invariant measures on generalised iterated function systems

Antti Käenmäki
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Abstract

We consider the limit set of generalised iterated function systems. Under the assumption of a natural potential, the so called cylinder function, we prove the existence of the invariant probability measure satisfying the equilibrium state. We motivate this approach by showing that for typical self-affine sets there exists an ergodic invariant measure having the same Hausdorff dimension as the set itself.

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Antti Käenmäki. 2017-01-30. On natural invariant measures on generalised iterated function systems. https://doi.org/10.5186/aasfm.00

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