Attractors for iterated function systems

DOI10.4171/JFG/31zbMath1345.28014OpenAlexW2347049842MaRDI QIDQ294292

Timothy H. Steele, D'Aniello, Emma

Publication date: 16 June 2016

Published in: Journal of Fractal Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/jfg/31

zbMATH Keywords

attractoriterated function systemself-similar settypical (according to Baire) element

Mathematics Subject Classification ID

Fractals (28A80) Iteration of real functions in one variable (26A18) Hausdorff and packing measures (28A78)

Related Items (13)

Size of the set of attractors for iterated function systems ⋮ Embedding fractals in Banach, Hilbert or Euclidean spaces ⋮ Porosities of the sets of attractors ⋮ Valuation theory, generalized IFS attractors and fractals ⋮ Comparison of the sets of attractors for systems of contractions and weak contractions ⋮ Attractors for classes of iterated function systems ⋮ Zero-dimensional compact metrizable spaces as attractors of generalized iterated function systems ⋮ Space-filling curves of self-similar sets (II): edge-to-trail substitution rule ⋮ Sums of convex compacta as attractors of hyperbolic IFS's ⋮ Non-self-similar sets in \([0,1^{N}\) of arbitrary dimension] ⋮ Attractor of Cantor type with positive measure ⋮ On a typical compact set as the attractor of generalized iterated function systems of infinite order ⋮ Borel complexity of the family of attractors for weak IFSs

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the structures of generating iterated function systems of Cantor sets
• The Lipschitz structure of continuous self-maps of generic compact sets
• A class of continua that are not attractors of any IFS
• The persistence of \(\omega\)-limit sets defined on compact spaces
• Ubiquity of odometers in topological dynamical systems
• Self-similarity in the collection of \(\omega \)-limit sets
• Attractors of Iterated Function Systems
• Separation Properties for Self-Similar Sets
• A 𝐶¹ function for which the 𝜔-limit points are not contained in the closure of the periodic points
• A 1-dimensional Peano continuum which is not an IFS attractor

This page was built for publication: Attractors for iterated function systems