On $δ$-deformations of polygonal dendrites

Drozdov, Dmitry; Samuel, Mary; Tetenov, Andrei

doi:10.48550/arxiv.1812.00439

Cited by 1 publication

(1 citation statement)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Among the possible types of dendrites there is a class known as polygonal dendrites that has been considered recently by Andrey Tetenov, Mary Samuel, and their collaborators [31]. The idea of δ-deformations of polygonal dendrites introduced in [32] is being captured by our notion of stable set K. Many polygonal dendrites can be associated to stable complex trees, for instance, δ-deformations also apply to tipsets of binary complex trees from the families obtained in ( 12), (13), and ( 14) as long as the tipset F A (z) is a structurally stable dendrite, i.e. z ∈ K, see figure 6.…”

Section: Polygonal Dendritesmentioning

confidence: 99%

Families of connected self-similar sets generated by complex trees

Espigule

2019

Preprint

View full text Add to dashboard Cite

The theory of complex trees is introduced as a new approach to study a broad class of self-similar sets. Systems of equations encoded by complex trees tip-to-tip equivalence relations are used to obtain oneparameter families of connected self-similar sets F A (z). In order to study topological changes of F A (z) in regions R ⊆ C where these families are defined, we introduce a new kind of set M ⊆ R which extends the usual notion of connectivity locus for a parameter space. Moreover we consider another set M 0 ⊂ M related to a special type of connectivity for which we provide a theorem. Among other things, the present theory provides a unified framework to families of self-similar sets traditionally studied as separate with elements F A (z) disconnected for parameters z ∈ R\M. Keywords complex trees • self-similar sets • IFSs • Hausdorff dimension • OSC • fractal dendrites • fractal trees

show abstract

Section: Polygonal Dendritesmentioning

confidence: 99%