Gromov Hyperbolic Graphs Arising From Iterations

Autor:	Kong, Shi-Lei, Lau, Ka-Sing, Wang, Xiang-Yang
Rok vydání:	2020
Předmět:	Mathematics - Metric Geometry Mathematics - Combinatorics Mathematics - Dynamical Systems 28A78 (Primary) 28A80 (Secondary)
Druh dokumentu:	Working Paper
Popis:	For a contractive iterated function system (IFS), it is known that there is a natural hyperbolic graph structure (augmented tree) on the symbolic space of the IFS that reflects the relationship among neighboring cells, and its hyperbolic boundary with the Gromov metric is H\"older equivalent to the attractor $K$. This setup was taken up to study the probabilistic potential theory on $K$, and the bi-Lipschitz equivalence on $K$. In this paper, we formulate a broad class of hyperbolic graphs, called expansive hyperbolic graphs, to capture the most essential properties from the augmented trees and the hyperbolic boundaries (e.g., the special geodesics, bounded degree property, metric doubling property, and H\"older equivalence). We also study a new setup of "weighted" IFS and investigate its connection with the self-similar energy form in the analysis of fractals. Comment: 32 pages, 9 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2006.12916 Zobrazit plný text záznamu View this record from Arxiv