A characterization of self-similar measures |
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| Affiliation: | 1. School of Sciences, Jimei University, Xiamen 361021, PR China;2. Department of Mathematics, Fujian Normal University, Fuzhou 350007, PR China;1. Department of Particle Physics and Astrophysics, Weizmann Institute of Science, 76100 Rehovot, Israel;2. LIBPhys, Department of Physics, University of Coimbra, RuaLarga, PT3004-516 Coimbra, Portugal;3. I3N, Physics Department, University of Aveiro, 3810-193 Aveiro, Portugal;4. CERN, Meyrin, Switzerland;1. State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, China;2. CNPC Chuanqing Drilling Engineering Co., LTD, China;1. Department of Mathematics, Tsinghua University, Beijing 100084, China;2. Department of Mathematics, University of Ulsan, Ulsan 680-749, Republic of Korea;3. School of Software, Tsinghua University, Key Laboratory for Information System Security, Ministry of Education of China, Beijing 100084, China;1. College of Mathematical and Physical Sciences, Taizhou University, Taizhou, 225300, China;2. School of Mathematical Sciences and Institute of Mathematics, Nanjing Normal University, Nanjing, 210023, China |
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| Abstract: | For a graph directed self-similar set, we investigate a list of invariant self-similar measures. In particular, the existence of the local dimension of the associated self-similar measure is determined. Consequently, the multifractal decomposition of the graph directed self-similar set can be formulated under the open set condition. This give a positive answer to a question posed by Edgar and Mauldin, as well as Olsen. |
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