论文标题
Markov间隔图的多重分析分析，具有许多分支
Multifractal analysis for Markov interval maps with countably many branches
论文作者
论文摘要
我们研究了基于Birkhoff平均值的多重分解分解，用于属于某些象征性连续函数的功能序列。我们为扩展的间隔图提供了此操作，并具有许多分支，我们假设可以通过拓扑混合可数的马尔可夫移动来编码。这将概括为以有限的许多分支扩展地图，并用数量有许多分支扩展地图，其中编码被认为是完整的变化。当每个分支上的衍生物的最大值接近限制的无穷大时，我们可以直接概括整个可计数转移情况的结果。但是，当这不成立时，我们表明可能存在不同的行为，特别是在编码具有有限拓扑熵的情况下。
We study multifractal decompositions based on Birkhoff averages for sequences of functions belonging to certain classes of symbolically continuous functions. We do this for an expanding interval map with countably many branches, which we assume can be coded by a topologically mixing countable Markov shift. This generalises previous work on expanding maps with finitely many branches, and expanding maps with countably many branches where the coding is assumed to be the full shift. When the infimum of the derivative on each branch approaches infinity in the limit, we can directly generalise the results of the full countable shift case. However, when this does not hold, we show that there can be different behaviour, in particular in cases where the coding has finite topological entropy.
