Hausdorff dimension of asymptotic self-similar sets

摘要

In this paper, we introduce the notion of asymptotic self-similar sets ongeneral doubling metric spaces by extending the notion of self-similar sets,and determine their Hausdorff dimensions, which gives an extension of Baloghand Rohner 's result. This is carried out by introducing the notions of almostsimilarity maps and asymptotic similarity systems. These notions have anadvantage of making geometric constructions possible. Actually, as anapplication, we determined the Hausdorff dimension of general Sierpinskigaskets on complete surfaces constructed by a geometric way in a naturalmanner.