Birkhoff平均在自仿射排斥子上的堆积谱
The packing spectrum for Birkhoff averages on a self-affine repeller
摘要：
本文研究了自仿射Sierpienski海绵上连续势的Birkhoff平均的多重分形分析。特别地，我们给出了一个变分原理的水平集的包装维数。此外，我们证明了填充谱是凹的和连续的。我们给出了填充谱是实解析的一个充分条件，但证明了对于一般的Hölder连续势，情况并非如此.我们还给出了一个精确的标准时，包装谱达到完整的包装尺寸的排斥。再次，我们提出了一个例子，表明这并不总是如此。
英文摘要：
We consider the multifractal analysis for Birkhoff averages of continuous potentials on a self-affine Sierpiński sponge. In particular, we give a variational principal for the packing dimension of the level sets. Furthermore, we prove that the packing spectrum is concave and continuous. We give a sufficient condition for the packing spectrum to be real analytic, but show that for general Hölder continuous potentials, this need not be the case. We also give a precise criterion for when the packing spectrum attains the full packing dimension of the repeller. Again, we present an example showing that this is not always the case.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
