منابع مشابه
Attractors of Iterated Function Systems
In this paper, the question of which compact metric spaces can be attractors of hyperbolic iterated function systems on Euclidean space is studied. It is shown that given any finite-dimensional compact metric X , there is a Cantor set C such that the disjoint union of C and X is an attractor. In the process, it is proved that every such X is the Lipschitz image of a Cantor set.
متن کاملAttractors of Sequences of Iterated Function Systems
If F and G are iterated function systems, then any infinite word W in the symbols F and G induces a limit set. It is natural to ask whether this Cantor set can also be realized as the limit set of a single C iterated function system H. We prove that under certain assumptions on F and G, the answer is no. This problem is motivated by the spectral theory of one-dimensional quasicrystals.
متن کاملExpectations over Attractors of Iterated Function Systems
Motivated by the need for new mathematical tools applicable to the study of fractal point-cloud distributions, expectations of complex-valued functions defined over general ‘deterministic’ fractal domains are considered, following the development of a measure-theoretic foundation for their analysis. In particular, we wish to understand and evaluate separation moments as given by integrals of th...
متن کاملConnectedness of the Attractors of Iterated Function Systems
We survey some of the topological properties of the attractors of iterated function systems such as connectedness, arcwise connectedness and locally arcwise connectedness. We give necessary and sufficient conditions for the attractors of finite iterated function system (IFS) to be a connected sets and in the case when infinite iterated function systems (IIFS) are considered we give only some su...
متن کاملEstimating the spatial extent of attractors of iterated function systems
From any given Iterated Function System, a small set of balls that cover the fractal attractor can be simply determined. This gives a priori bounds on the region of space in which the attractor may be constructed.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1992
ISSN: 0002-9939
DOI: 10.2307/2159324