Preprint
IFS measures on generalized Bratteli diagrams
ArXiv.org
10/25/2022
DOI: 10.48550/arXiv.2210.14059
Abstract
The purpose of the paper is a general analysis of path space
measures. Our focus is a certain path space analysis
on generalized Bratteli diagrams. We use this in a systematic study of
systems of self-similar measures (the term ``IFS measures'' is used in the
paper) for both types of such diagrams, discrete and continuous. In special
cases, such measures arise in the study of iterated function
systems (IFS). In the literature, similarity may be defined by,
e.g., systems of affine maps (Sierpinski), or systems of conformal
maps (Julia). We study new classes of semi-branching
function systems related to stationary Bratteli diagrams. The
latter plays a big role in our understanding
of new forms of harmonic analysis on fractals. The measures
considered here arise in classes of discrete-time, multi-level
dynamical systems where similarity is specified between levels.
These structures are made precise by prescribed systems of
functions which in turn serve to define self-similarity, i.e., the similarity
of large scales, and small scales.
For path space systems, in our main result, we give a necessary and
sufficient condition for the existence of such generalized IFS measures. For
the corresponding semi-branching function systems, we further identify the
measures which are also shift-invariant.
Details
- Title: Subtitle
- IFS measures on generalized Bratteli diagrams
- Creators
- Sergey BezuglyiPalle E. T Jorgensen
- Resource Type
- Preprint
- Publication Details
- ArXiv.org
- DOI
- 10.48550/arXiv.2210.14059
- ISSN
- 2331-8422
- Language
- English
- Date posted
- 10/25/2022
- Academic Unit
- Mathematics
- Record Identifier
- 9984310139602771
Metrics
23 Record Views