Search results for "Inductive dimension"

showing 2 items of 2 documents

Local dimensions of measures on infinitely generated self-affine sets

2014

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.

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 dimensionulottuvuudetAnalysisMathematicsJournal of Mathematical Analysis and Applications
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Separation properties of (n, m)-IFS attractors

2017

Abstract The separation properties of self similar sets are discussed in this article. An open set condition for the (n, m)- iterated function system is introduced and the concepts of self similarity, similarity dimension and Hausdorff dimension of the attractor generated by an (n, m) - iterated function system are studied. It is proved that the similarity dimension and the Hausdorff dimension of the attractor of an (n, m) - iterated function system are equal under this open set condition. Further a necessary and sufficient condition for a set to satisfy the open set condition is established.

Numerical AnalysisApplied Mathematics010102 general mathematicsMathematicsofComputing_NUMERICALANALYSISMinkowski–Bouligand dimensionDimension functionEffective dimension01 natural sciences010101 applied mathematicsCombinatoricsPacking dimensionCollage theoremModeling and SimulationHausdorff dimensionHausdorff measure0101 mathematicsInductive dimensionMathematicsCommunications in Nonlinear Science and Numerical Simulation
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