Generalized dimensions of measures on self-affine sets

被引：42
|
作者：
Falconer, KJ [1 ]
机构：
[1] Univ St Andrews, Math Inst, St Andrews KY16 9SS, Fife, Scotland
来源：
NONLINEARITY | 1999年 / 12卷 / 04期
关键词：
D O I：
10.1088/0951-7715/12/4/308
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We obtain bounds for the generalized q-dimensions of measures supported by self-affine sets that ate valid for 'almost all' families of affine mappings. Exact values are established for self-affine measures and for Gibbs measures when 1 < q less than or equal to 2. These q-dimensions may exhibit phase transitions as q varies.
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页码：877 / 891
页数：15
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