Multifractal analysis of Birkhoff averages for countable Markov maps
Multifractal analysis of Birkhoff averages for countable Markov maps
复制标题
DOI：
10.1017/etds.2015.44
复制
发表时间：
2010-03
影响因子：
0.9
通讯作者：
G. Iommi;T. Jordan
中科院分区：
文献类型：
--
作者：
G. Iommi;T. Jordan
本文证明了具有可数分支的区间映射Birkhoff平均的重分形形式。进一步证明了在一定的假设下Birkhoff谱是真实的解析的.我们还表明，新的现象发生，事实上，频谱可以是恒定的，或者它可以有点，它不是分析。获得了这些发生的条件。这些结果的应用数论也给出。最后，我们计算的Hausdorff维数的点集的Birkhoff平均是无限的。
In this paper we prove a multifractal formalism of Birkhoff averages for interval maps with countably many branches. Furthermore, we prove that under certain assumptions the Birkhoff spectrum is real analytic. We also show that new phenomena occur; indeed, the spectrum can be constant or it can have points where it is not analytic. Conditions for these to happen are obtained. Applications of these results to number theory are also given. Finally, we compute the Hausdorff dimension of the set of points for which the Birkhoff average is infinite.