Dimension of invariant measures for affine iterated function systems

نویسندگان

چکیده

Let {Si}i∈Λ be a finite contracting affine iterated function system (IFS) on Rd. (Σ,σ) denote the two-sided full shift over alphabet Λ, and let π:Σ→Rd coding map associated with IFS. We prove that projection of an ergodic σ-invariant measure Σ under π is always exact dimensional, its Hausdorff dimension satisfies Ledrappier–Young-type formula. Furthermore, result extends to average IFSs. This completes several previous results answers folklore open question in community fractals. Some applications are given self-affine sets measures.

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ژورنال

عنوان ژورنال: Duke Mathematical Journal

سال: 2023

ISSN: ['1547-7398', '0012-7094']

DOI: https://doi.org/10.1215/00127094-2022-0014