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
@article{bwmeta1.element.doi-10_1515_wwfaa-2017-0008,
author = {Amit Priyadarshi},
title = {Infinite Graph-Directed Systems and Hausdorff Dimension},
journal = {Waves, Wavelets and Fractals},
volume = {3},
year = {2017},
pages = {84-95},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_wwfaa-2017-0008}
}
Amit Priyadarshi. Infinite Graph-Directed Systems and Hausdorff Dimension. Waves, Wavelets and Fractals, Tome 3 (2017) pp. 84-95. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_wwfaa-2017-0008/