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DIMENSIONAL APPROXIMATION OF AN INHOMOGENEOUS ATTRACTOR WITHOUT ANY SEPARATION CONDITION
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Classical measure theory
Published online by Cambridge University Press: 23 June 2025
Abstract
We show that the Hausdorff dimension of the attractor of an inhomogeneous self-similar iterated function system (or self-similar IFS) can be well approximated by the Hausdorff dimension of the attractor of another inhomogeneous self-similar IFS satisfying the strong separation condition. We also determine a formula for the Hausdorff dimension of the algebraic product and sum of the inhomogeneous attractor.
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- © The Author(s), 2025. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc
Footnotes
The Author acknowledges support from the grant NKFI KKP144059 ‘Fractal geometry and applications’.
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