REGULARITY OF MULTIFRACTAL SPECTRA OF CONFORMAL ITERATED FUNCTION SYSTEMS
REGULARITY OF MULTIFRACTAL SPECTRA OF CONFORMAL ITERATED FUNCTION SYSTEMS
复制标题
共形迭代函数系统的多重分形谱的正则性
DOI：
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发表时间：
2009
期刊：
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通讯作者：
Marc Kessebohmer
中科院分区：
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作者：
Johannes Jaerisch;Marc Kessebohmer
研究了无穷共形迭代函数系统（cIFS）的多重分形正则性.即我们确定多重分形谱在多大程度上连续依赖于cIFS及其热力学势。为此，我们引入了cIFS族的正则收敛的概念，这类cIFS族不必共享相同的指标集，从而保证了多重分形谱在其定义域内部的收敛性.特别是，我们得到了一个穷尽原则无限cIFS允许我们结转有限到无限系统的结果，并以这种方式建立一个多重分形分析没有通常的正则性条件。最后，我们讨论了Roy和Urba ′ nski引入的λ-拓扑的连接。
We investigate multifractal regularity for infinite conformal iterated function systems (cIFS). That is we determine to what extent the multifractal spectrum depends continuously on the cIFS and its thermodynamic potential. For this we introduce the no- tion of regular convergence for families of cIFS not necessarily sharing the same index set, which guarantees the convergence of the multifractal spectra on the interior of their domain. In particular, we obtain an Exhausting Principle for infinite cIFS allowing us to carry over results for finite to infinite systems, and in this way to establish a multifractal analysis without the usual regularity conditions. Finally, we discuss the connections to the λ-topology introduced by Roy and Urba´ nski.