A class of iterated function systems with adapted piecewise constant transition probabilities: asymptotic stability and Hausdorff dimension of the invariant measure

DOI10.1016/J.CHAOS.2017.05.024zbMath1375.60115OpenAlexW2736387485MaRDI QIDQ1681724

Blandine Dubarry

Publication date: 24 November 2017

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.chaos.2017.05.024

zbMATH Keywords

asymptotic stabilityHausdorff dimensioninvariant measurefractalsMarkov operatorsiterated function systems

Mathematics Subject Classification ID

Discrete-time Markov processes on general state spaces (60J05) Ergodic theorems, spectral theory, Markov operators (37A30) Fractals (28A80) Symbolic dynamics (37B10) Hausdorff and packing measures (28A78)

Cites Work

• On the Hausdorff dimension of invariant measures of weakly contracting on average measurable IFS
• Invariant measures for Markov processes arising from iterated function systems with place-dependent probabilities
• Iterated function system and Ruelle operator
• On measures driven by Markov chains
• A note on iterated function systems with discontinuous probabilities
• ERGODICITY, UNIDIMENSIONALITY AND MULTIFRACTALITY OF SELF-SIMILAR MEASURES
• The stability of Markov operators on Polish spaces
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