Infinite Graph-Directed Systems and Hausdorff Dimension

Amit Priyadarshi. "Infinite Graph-Directed Systems and Hausdorff Dimension." Waves, Wavelets and Fractals 3.1 (2017): 84-95. <http://eudml.org/doc/288386>.

@article{AmitPriyadarshi2017,
abstract = {In this paper we study infinite graph-directed iterated function systems on compact metric spaces given by contractive ‘infinitesimal similitudes’. We derive formula for the Hausdorff dimension of the ‘invariant set’ for such a system in terms of the spectral radii of the naturally associated family of the ‘Perron- Frobenius operators’. The results in this paper generalizes the results obtained in [20], where finite graphdirected systems and infinite iterated function systems are considered},
author = {Amit Priyadarshi},
journal = {Waves, Wavelets and Fractals},
keywords = {Hausdorff dimension; iterated function systems; graph-directed systems; Perron-Frobenius operators; spectral radius},
language = {eng},
number = {1},
pages = {84-95},
title = {Infinite Graph-Directed Systems and Hausdorff Dimension},
url = {http://eudml.org/doc/288386},
volume = {3},
year = {2017},
}

TY - JOUR
AU - Amit Priyadarshi
TI - Infinite Graph-Directed Systems and Hausdorff Dimension
JO - Waves, Wavelets and Fractals
PY - 2017
VL - 3
IS - 1
SP - 84
EP - 95
AB - In this paper we study infinite graph-directed iterated function systems on compact metric spaces given by contractive ‘infinitesimal similitudes’. We derive formula for the Hausdorff dimension of the ‘invariant set’ for such a system in terms of the spectral radii of the naturally associated family of the ‘Perron- Frobenius operators’. The results in this paper generalizes the results obtained in [20], where finite graphdirected systems and infinite iterated function systems are considered
LA - eng
KW - Hausdorff dimension; iterated function systems; graph-directed systems; Perron-Frobenius operators; spectral radius
UR - http://eudml.org/doc/288386
ER -