Resonance between planar self-affine measures

We show that if { phi i } i is an element of Gamma and { 0 j } j is an element of Lambda are self-affine iterated function systems on the plane that satisfy strong separation, domination and irreducibility, then for any associated selfaffine measures mu and v, the inequality dim H ( mu & lowast; v ) sigma min {2, dim H mu + dim H v } implies that there is algebraic resonance between the eigenvalues of the linear parts of phi i and 0 j . This extends to planar non-conformal setting the existing analogous results for self-conformal measures on the line. (c) 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/).