The Scenery Flow for Self-Affine Measures
Tom Kempton
TL;DR
This paper investigates the scaling scenery of Bernoulli measures on separated self-affine sets, focusing on cases where certain projections are absolutely continuous, to understand their geometric and measure-theoretic properties.
Contribution
It introduces a novel analysis of the scaling scenery for self-affine measures under specific projection conditions, advancing understanding of their local structure.
Findings
Characterization of the scaling scenery for Bernoulli measures on self-affine sets.
Conditions under which projections of these measures are absolutely continuous.
Insights into the local geometric structure of self-affine measures.
Abstract
We describe the scaling scenery associated to Bernoulli measures supported on separated self-affine sets under the condition that certain projections of the measure are absolutely continuous.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Topological and Geometric Data Analysis · Theoretical and Computational Physics