Year: 2023
Type: paratext
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.
DOI: 10.5186/aasfm.00
Author: K\"aenm\"aki, Antti
Language: Latin
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W107627188