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- W1899970382 abstract "Let $left { f_iright } _{i=1}^N$ be a family of $N$ contractive mappings on $mathbb {R}^{dtext { }}$ such that the attractor $K$ has nonvoid interior. We show that if the $f_i$âs are injective, have non-vanishing Jacobian on $K$, and $f_ileft ( Kright ) cap f_jleft ( Kright )$ have zero Lebesgue measure for $ineq j,$ then the boundary $partial K$ of $K$ has measure zero. In addition if the $f_i$âs are affine maps, then the conclusion can be strengthened to $dim _Hleft ( partial Kright ) <d$. These improve a result of Lagarias and Wang on self-affine tiles." @default.
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- W1899970382 date "1999-10-27" @default.
- W1899970382 modified "2023-10-18" @default.
- W1899970382 title "On the boundary of attractors with non-void interior" @default.
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- W1899970382 doi "https://doi.org/10.1090/s0002-9939-99-05303-4" @default.
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