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Stationary measures associated to analytic iterated function schemes

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  • Italo Cipriano
  • Mark Pollicott

Abstract

We study how the stationary measure associated to analytic contractions on the unit interval behaves under changes in the contractions and the weights. Firstly we give a simple proof of the fact that the integrals of analytic functions with respect to the stationary measure vary analytically if we perturb the contractions and the weights analytically. Secondly, we consider the special case of affine contractions and we prove a conjecture of J. Fraser in on the Kantorovich–Wasserstein distance between two stationary measures associated to affine contractions on the unit interval with different rates of contraction.

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  • Italo Cipriano & Mark Pollicott, 2018. "Stationary measures associated to analytic iterated function schemes," Mathematische Nachrichten, Wiley Blackwell, vol. 291(7), pages 1049-1054, May.
    • Handle: RePEc:bla:mathna:v:291:y:2018:i:7:p:1049-1054
    DOI: 10.1002/mana.201600127
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    Cited by:

    1. Easton Brawley & Mason Doyle & Robert Niedzialomski, 2022. "On the 2‐Wasserstein distance for self‐similar measures on the unit interval," Mathematische Nachrichten, Wiley Blackwell, vol. 295(3), pages 468-486, March.

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