Connectedness of the Attractors of Iterated Function Systems
نویسندگان
چکیده
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 sufficient conditions. Attractors with many connected components are also considered in the case of IFSs. We also describe the shift space associated to an attractor. Some examples are given for each considered case.
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