On dendrites, generated by polyhedral systems and their ramification points

2017/07/07 by Andrei Tetenov, Tetenov, Andrei, Mary Samuel +3
Mathematics · #28A80 #Advanced Differential Equations and Dynamical Systems #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.1707.02875

openalex publication_date 2017/07/07 · openalex created_date 2017/07/21 · openalex updated_date 2026/07/28

Abstract

The paper considers systems of contraction similarities in \mathbb R^d sending a given polyhedron P to polyhedra P_i⊂ P, whose non-empty intersections are singletons and contain the common vertices of those polyhedra, while the intersection hypergraph of the system is acyclic. It is proved that the attractor K of such system is a dendrite in \mathbb R^d. The ramification points of such dendrite fave finite order whose upper bound depends only on the polyhedron P, and the set of the cut points of the dendrite K is equal to the dimension of the whole K iff K is a Jordan arc.

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