Resonance between planar self-affine measures
Pyörälä, Aleksi (2024-06-14)
Elsevier
14.06.2024
Pyörälä, A. (2024). Resonance between planar self-affine measures. Advances in Mathematics, 451, 109770. https://doi.org/10.1016/j.aim.2024.109770
https://creativecommons.org/licenses/by/4.0/
© 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org /licenses /by /4 .0/).
https://creativecommons.org/licenses/by/4.0/
© 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org /licenses /by /4 .0/).
https://creativecommons.org/licenses/by/4.0/
Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi:oulu-202411126723
https://urn.fi/URN:NBN:fi:oulu-202411126723
Tiivistelmä
Abstract
We show that if {ϕi}i∈Γ and {ψj }j∈Λ are self-affine iterated function systems on the plane that satisfy strong separation, domination and irreducibility, then for any associated self-affine measures μ and ν, the inequality
dimH(μ ∗ ν) < min{2, dimH μ + dimH ν}
implies that there is algebraic resonance between the eigenvalues of the linear parts of ϕi and ψj . This extends to planar non-conformal setting the existing analogous results for self-conformal measures on the line.
We show that if {ϕi}i∈Γ and {ψj }j∈Λ are self-affine iterated function systems on the plane that satisfy strong separation, domination and irreducibility, then for any associated self-affine measures μ and ν, the inequality
dimH(μ ∗ ν) < min{2, dimH μ + dimH ν}
implies that there is algebraic resonance between the eigenvalues of the linear parts of ϕi and ψj . This extends to planar non-conformal setting the existing analogous results for self-conformal measures on the line.
Kokoelmat
- Avoin saatavuus [38840]
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