Acta mathematica scientia,Series B
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Yu Jinghu; Shieh Narn-Rueih
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Abstract:
Given a system {S1,…, SN} of N contractive similarities satisfying some strong separation condition, it has an invariant set K for the system. In this article, the authors construct some random measure $\mu_\o$ supported on random subset $K_\o$ of $K$, $\mu_\o$ having some "non-standard" multifractal structure, which contrasts the well-known multifractal formalism for the invariant measure of system {S1,…, SN} may possess. The main tool is the multifractal structures of a Galton-Watson tree, which are obtained by Liu [9], Shieh--Taylor [14], and Morters--Shieh [12].
Key words: Multifraetal structure, iterated function styslem, Galton-Watson tree
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Yu Jinghu; Shieh Narn-Rueih. ITERATED FUNCTION SYSTEM AND GALTON-WATSON TREE[J].Acta mathematica scientia,Series B, 2007, 27(3): 456-464.
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URL: http://121.43.60.238/sxwlxbB/EN/10.1016/S0252-9602(07)60046-0
http://121.43.60.238/sxwlxbB/EN/Y2007/V27/I3/456
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