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 inequalitydimH(μ⁎ν)<min{2,dimHμ+dimHν} 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.
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