RT Journal Article
T1 Local Geometry of Self-similar Sets: Typical Balls, TangentMeasures and Asymptotic Spectra.
T2 Geometría local de conjuntos autosemejantes: bolas típicas, medidas tangentes y espectro asintótico
A1 Mera Rivas, María Eugenia
A1 Llorente Comi, Marta
A1 Morán Cabré, Manuel
AB We analyze the local geometric structure of self-similar sets with open set condition through the study of the properties of a distinguished family of spherical neighborhoods, the typical balls. We quantify the complexity of the local geometry of self-similar sets, showing that there are uncountably many classes of spherical neighborhoods that are not equivalent under similitudes. We show that at a tangent level, the uniformity of the Euclidean space is recuperated in the sense that any typical ball is a tangent measure of the measure at mu-a.e. point, where mu is any self-similar measure. We characterize the spectrum of asymptotic densities of metric measures in terms of the packing and centered Hausdorff measures. As an example, we compute the spectrum of asymptotic densities of the Sierpiński gasket.
PB World Scientific
SN 0218-348X
YR 2023
FD 2023
LK https://hdl.handle.net/20.500.14352/94994
UL https://hdl.handle.net/20.500.14352/94994
LA eng
NO Morán M., Llorente M., Mera M.E.  Local geometry of self-similar sets: typical balls, tangent measures and asympotic spectra. Fractals Vol. 31, No. 05, 2350059 (2023)
NO Universidad Complutense de Madrid 
DS Docta Complutense
RD 9 abr 2025