TY - JOUR

T1 - Intersections of the pieces of self-similar dendrites in the plane

AU - Allabergenova, Klara

AU - Samuel, Mary

AU - Tetenov, Andrei

N1 - The work is supported by the Mathematical Center in Akademgorodok under the agreement no. 075-15-2022-281 with the Ministry of Science and Higher Education of the Russian Federation.

PY - 2024/5

Y1 - 2024/5

N2 - We prove that each self-similar dendrite in the plane has the weak separation property and that the ramificationorders of its points are bounded. We show that there are self-similar dendrites in the plane that satisfy theOpen Set Condition, such that several pieces may intersect in the same non-trivial subdendrite.

AB - We prove that each self-similar dendrite in the plane has the weak separation property and that the ramificationorders of its points are bounded. We show that there are self-similar dendrites in the plane that satisfy theOpen Set Condition, such that several pieces may intersect in the same non-trivial subdendrite.

KW - Self-similar set

KW - Dendrite

KW - Open set condition

KW - Weak separation property

KW - Intersection graph

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85189510586&origin=inward&txGid=3f219771c8ea51c6505b81d061964c35

U2 - 10.1016/j.chaos.2024.114805

DO - 10.1016/j.chaos.2024.114805

M3 - Article

VL - 182

JO - Chaos, Solitons and Fractals

JF - Chaos, Solitons and Fractals

SN - 0960-0779

M1 - 114805

ER -