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Local dimensions of measures on infinitely generated self-affine sets

Eino Rossi

subject

Discrete mathematicsmatematiikka28A80Applied Mathematicsta111Minkowski–Bouligand dimensionDimension functionMetric Geometry (math.MG)Dynamical Systems (math.DS)Complex dimensionEffective dimensionPacking dimensionMathematics - Metric GeometryHausdorff dimensionFOS: MathematicsdimensionsMathematics - Dynamical SystemsDimension theory (algebra)Inductive dimensionulottuvuudetAnalysisMathematics

description

We show the existence of the local dimension of an invariant probability measure on an infinitely generated self-affine set, for almost all translations. This implies that an ergodic probability measure is exactly dimensional. Furthermore the local dimension equals the minimum of the local Lyapunov dimension and the dimension of the space. We also give an estimate, that holds for all translation vectors, with only assuming the affine maps to be contractive.

yearjournalcountryeditionlanguage
2014-01-01Journal of Mathematical Analysis and Applications
10.1016/j.jmaa.2013.12.030http://juuli.fi/Record/0028781414