Iterated Function Systems Enriched with Symmetry

2021 ◽  
Author(s):  
Krzysztof Leśniak ◽  
Nina Snigireva
Keyword(s):  
Iterated Function Systems ◽  
Iterated Function

scholarly journals Hausdorff measure and Assouad dimension of generic self-conformal IFS on the line

2020 ◽  
pp. 1-31
Author(s):  
Balázs Bárány ◽  
Károly Simon ◽  
István Kolossváry ◽  
Michał Rams
Keyword(s):  
Hausdorff Measure ◽  
Similar Case ◽  
Iterated Function Systems ◽  
The Self ◽  
Dimensional Hausdorff Measure ◽  
Assouad Dimension ◽  
Iterated Function ◽  
Self Similar ◽  
Weak Separation ◽  
Topological Sense

This paper considers self-conformal iterated function systems (IFSs) on the real line whose first level cylinders overlap. In the space of self-conformal IFSs, we show that generically (in topological sense) if the attractor of such a system has Hausdorff dimension less than 1 then it has zero appropriate dimensional Hausdorff measure and its Assouad dimension is equal to 1. Our main contribution is in showing that if the cylinders intersect then the IFS generically does not satisfy the weak separation property and hence, we may apply a recent result of Angelevska, Käenmäki and Troscheit. This phenomenon holds for transversal families (in particular for the translation family) typically, in the self-similar case, in both topological and in measure theoretical sense, and in the more general self-conformal case in the topological sense.

Iterated function systems and dynamical systems

1995 ◽  
Vol 5 (4) ◽  
pp. 634-639 ◽  
Author(s):  
Pawel/ Góra ◽  
Abraham Boyarsky
Keyword(s):  
Dynamical Systems ◽  
Iterated Function Systems ◽  
Iterated Function
Sign in / Sign up

Export Citation Format

Share Document