On hyperbolic graphs induced by iterated function systems
Publication in refereed journal

香港中文大學研究人員

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其它資訊
摘要For any contractive iterated function system (IFS, including the Moran systems), we show that there is a natural hyperbolic graph on the symbolic space, which yields the Hölder equivalence of the hyperbolic boundary and the invariant set of the IFS. This completes the previous studies ([16]; [20] ; [30]) by eliminating superfluous conditions, and admits more classes of sets (e.g., the Moran sets). We also show that the bounded degree property of the graph can be used to characterize certain separation properties of the IFS (open set condition, weak separation condition); the bounded degree property is particularly important when we consider random walks on such graphs. This application and the other application to Lipschitz equivalence of self-similar sets will be discussed.
著者Ka-Sing Lau, Xiang-Yang Wang
期刊名稱Advances in Mathematics
出版年份2017
月份6
卷號313
頁次357 - 378
國際標準期刊號0001-8708
電子國際標準期刊號1090-2082
語言美式英語
關鍵詞Hyperbolic graphs, Hyperbolic boundaries, Iterated function systems, Self-similar sets, Open set condition, Weak separation condition

上次更新時間 2021-01-03 於 01:30