The example of a self-similar continuum which is not an attractor of any zipper
O. Purevdorj (Hovd university, Mongolia), A. V. Tetenov (Gorno-Altaisk, state university, Russian Federation)
TL;DR
This paper constructs a specific self-similar dendrite that defies being an attractor for any self-similar zipper, highlighting limitations in the attractor theory of self-similar structures.
Contribution
It introduces a novel example of a self-similar dendrite that cannot be realized as an attractor of any self-similar zipper, expanding understanding of self-similar set limitations.
Findings
Constructed a self-similar dendrite not an attractor of any zipper
Demonstrated limitations of self-similar zipper attractors
Provides a new example in self-similar set theory
Abstract
The article contains a construction of a self-similar dendryte which cannot be the attractor of any self-similar zipper.
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Taxonomy
TopicsEngineering and Agricultural Innovations