ON THE GEOMETRIC STRUCTURE OF THE LIMIT SET OF CONFORMAL ITERATED FUNCTION SYSTEMS

We consider infinite conformai function systems on ℝd. We study the geometric structure of the limit set of such systems. Suppose this limit set intersects some l-dimensional C¹-submanifold with positive Hausdorff t-dimensional measure, where 0 < l < d and t is the Hausdorff dimension of the l...

Full description

Saved in:
Bibliographic Details
Published in:Publicacions matemàtiques 2003-01, Vol.47 (1), p.133-141
Main Author: Käenmäki, Antti
Format: Article
Language:English
Subjects:
Conformity
Fractals
Geometric planes
Iterations of functions
Mathematical theorems
Citations: Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We consider infinite conformai function systems on ℝd. We study the geometric structure of the limit set of such systems. Suppose this limit set intersects some l-dimensional C¹-submanifold with positive Hausdorff t-dimensional measure, where 0 < l < d and t is the Hausdorff dimension of the limit set. We then show that the closure of the limit set belongs to some l-dimensional affine subspace or geometric sphere whenever d exceeds 2 and analytic curve if d equals 2.
ISSN:0214-1493
2014-4350
DOI:10.5565/PUBLMAT_47103_06