2020
DOI: 10.26493/2590-9770.1375.12a
|View full text |Cite
|
Sign up to set email alerts
|

On deformation of polygonal dendrites preserving the intersection graph

Abstract: Let S = S 1 , ..., S m be a system of contracting similarities of R 2 . The attractor K(S) of the system S is a non-empty compact set satisfying K = S 1 (K) ∪ ... ∪ S m (K). We consider contractible polygonal systems S which are defined by a finite family of polygons whose intersection graph is a tree and therefore the attractor K(S) is a dendrite. We find conditions under which a deformation S of a contractible polygonal system S has the same intersection graph and therefore the attractor K(S ) is a self-simi… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
1
1

Citation Types

0
2
0

Year Published

2024
2024
2024
2024

Publication Types

Select...
1

Relationship

0
1

Authors

Journals

citations
Cited by 1 publication
(2 citation statements)
references
References 12 publications
(14 reference statements)
0
2
0
Order By: Relevance
“…There are a lot of recent papers on fractal squares, mainly by Chinese authors. See [15,24,34,42,43,[50][51][52] and their references. The automaton for fractal squares is the same as for the corresponding square, with fewer edge labels.…”
Section: More Examplesmentioning
confidence: 99%
See 1 more Smart Citation
“…There are a lot of recent papers on fractal squares, mainly by Chinese authors. See [15,24,34,42,43,[50][51][52] and their references. The automaton for fractal squares is the same as for the corresponding square, with fewer edge labels.…”
Section: More Examplesmentioning
confidence: 99%
“…So we must ask for characteristic exponents rather than absolute invariants. A first step would be to characterize contractible spaces which include trees [15] and disk-like tiles [1,29,32,49].…”
Section: Elementary Fractal Geometrymentioning
confidence: 99%