Slow and fast convergence to local dimensions of self-similar measures

✍ Scribed by L. Olsen

• Publisher: John Wiley and Sons
• Year: 2004
• Tongue: English
• Weight: 205 KB
• Volume: 266
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.200310145

✦ Synopsis

Let K and µ be the self-similar set and the self-similar measure associated with an iterated function system with probabilities (Si, pi)i=1,...,N satisfying the Open Set Condition. Let Σ = {1, . . . , N} N denote the full shift space and let π : Σ → K denote the natural projection. The (symbolic) local dimension of µ at ω ∈ Σ is defined by limn log µK ω|n log diam K ω|n