On the uniform doubling of Hutchinson orbits of contractive mappings

AIMAR HUGO, CARENA MARILINA, IAFFEI BIBIANA

Cuadernos de Matemática y Mecánica

CIMEC-IMAL

Año: 2008 p. 1 - 13

    Abstract. We are interested in the preservation of doubling properties alongthe Hutchinson orbit generated by successive applications of contraction map-pings on a metric measure space. We construct some elementary examples,built on Muckenhoupt weights, showing that even when the initial and thelimit points of the orbit are doubling, no iteration of the IFS remains dou-bling. We also obtain positive results under some quantitative assumptionson the separation of the images through the IFS. We also explore the com-pleteness, in the Hausdorff-Kantorovich metric, of a version of the doublingproperty which is suitable for the application of Hutchinson type contractions.