一类Moran测度的重分形谱
摘要
证明一类支撑在某些Moran分形上的Moran测度的重分形形式成立.
出处
《中国科学(A辑)》
CSCD
北大核心
2005年第2期147-161,共15页
Science in China(Series A)
基金
国家自然科学基金(批准号:10171028)中国科学院晨兴数学中心资助项目
参考文献16
-
1Falconer K J. Fractal Geometry: Mathematical Foundations and Applications. London: John Wiley & Sons, 1990.
-
2Feder J. Fractals. New York: Plenum Press, 1988.
-
3Halsey T C, Jenson M H, Kadanoff L P, et al. Fractal measures and their singularities: The characterization of strange sets. Phys Rev Let, 1986, A33: 1141-llS1.
-
4Bohr T, Rand D. The entropy function for characteristic exponents. Physica D, 1987, 25:387-393.
-
5Collet P, Lebowitz J L, Porzio A. The dimension spectrum of some dynamical systems. J Stat Phys, 1987,47:609-644.
-
6Pesin Y, Weiss H. The multifractal analysis of Gibbs measures: Motivation, mathematical foundation, and examples. Chaos, 1997, 7:89-106.
-
7Rand D. The singularity spectrum for cookie-cutters. Ergodic Theory Dynamical Systems, 1989, 9:527-541.
-
8Cawely R, Mauldin R D. Multifractal decompositions of Moran fractals. Adv Math, 1992, 92:196-236.
-
9Edgar G A, Mauldin R D. Multifractal decompositions of digraph recursive fractals. Proc London Math Soc, 1992, 65:604-628.
-
10Wu Min. The singularity spectrum f(a) of some Moran fractals. Monatshefte ftir Mathematik, 27 October, 2004. DOI: 10.1007/s00605-004-0254-3.
-
1肖加清.一类Moran测度的L^q-谱[J].应用数学,2007,20(3):462-466. 被引量:1
-
2肖加清.一类Moran测度的Hentschel-Procaccia维数[J].数学杂志,2009,29(3):307-312.
-
3吴敏.关于测度的重分形分析[J].华南理工大学学报(自然科学版),2012,40(10):142-145.
-
4郭红文.有限交性质及相关的分形维数[J].纺织高校基础科学学报,2001,14(2):144-146.
-
5陈二才,熊金城.关于自相似测度的点态维数[J].科学通报,1998,43(20):2162-2167. 被引量:1
-
6李文侠.一类集合的Hausdorff测度性质[J].华中师范大学学报(自然科学版),1994,28(3):286-288.
-
7余翠娥,吴敏.一类Moran测度的勒让德谱与q-Renyi维数[J].湖北大学学报(自然科学版),2007,29(2):121-125.
-
8束琳.双Lipschitz条件下自相似测度的维数估计[J].南京师大学报(自然科学版),2003,26(2):32-35.
-
9苏峰,赵兴球.广义自相似集的重fractal分解集的点态维数及packing维数[J].数学杂志,1995,15(4):396-400.
-
10李文侠.MoranFractals的推广及其多重分形分解[J].数学学报(中文版),1995,38(4):553-558.