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Self-similar dendrites generated by polygonal systems in the plane. (English) Zbl 1371.28028

Summary: We define a class of self-similar dendrites in \(\mathbb R^2\) generated by system \(\mathcal S\) of similarity maps of a convex polygon \(P\) and find upper bound for the order of their ramification points, show that such dendrites are continua of bounded turning and prove Hölder continuity of their isomorphisms.

MSC:

28A80 Fractals

Software:

IFStile
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