Stationary measures associated to analytic iterated function schemes. Issue 7 (3rd April 2018)

• Record Type: Journal Article
• Authors: Cipriano, Italo; Pollicott, Mark
• Is Part Of: Mathematische Nachrichten. Volume 291:Issue 7(2018)
• Page Start: 1049
• Page End: 1054
• Publication Date: 2018-04-03
• Subjects: self‐similar measure -- Wasserstein metric -- Please provide MSC (2010); Mathematics -- Periodicals; 510.5
• DOI: 10.1002/mana.201600127
• Languages: English
• ISSNs: 0025-584X

Abstract

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 in3 on the Kantorovich–Wasserstein distance between two stationary measures associated to affine contractions on the unit interval with different rates of contraction.