Polytechnic University of Valencia Congress, Workshop Applied Topological Structures WATS'17

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Irreducible fractal structures for Moran's theorems
Manuel Fernández-Martínez, Miguel Ángel Sánchez-Granero

Last modified: 01-10-2019

Abstract


Along this talk, we shall deal with a classical problem in Fractal Geometry consisting of the calculation of the similarity dimension of self-similar sets. Clasically, the open set condition has been understood as the right separation condition for IFS-attractors since it becomes a sufficient (though not necessary) condition allowing to easily calculate their similarity dimensions. However, it depends on an external open set.


Our contribution consists of a novel separation condition for self-similar sets we shall characterize in terms of the natural fractal structure which any IFS-attractor can be endowed with. We justify that such a separation condition is weaker than the strong open set condition and allows to prove some Moran's type theorems.


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