论文标题
纯点衍射和欧几里得空间以外的熵
Pure point diffraction and entropy beyond the Euclidean space
论文作者
论文摘要
对于有限的局部复杂性和均匀的贴片频率的欧几里得纯点衍射Delone集，众所周知，沿着封闭的中心球计算的斑块计数熵为零。我们在Sigma-Corcact局部紧凑的Abelian组的设置中考虑此类集合，并表明相关Delone动力学系统的拓扑熵为零。为此，我们提供了适当的变分原理版本。我们进一步构建反例，这表明在此上下文中，此类集合的补丁计数熵可能不是零。其他反例将表明，该集合的补丁计数熵无法按限制计算，甚至在这种情况下甚至是无限的。
For Euclidean pure point diffractive Delone sets of finite local complexity and with uniform patch frequencies it is well known that the patch counting entropy computed along the closed centred balls is zero. We consider such sets in the setting of sigma-compact locally compact Abelian groups and show that the topological entropy of the associated Delone dynamical system is zero. For this we provide a suitable version of the variational principle. We furthermore construct counterexamples, which show that the patch counting entropy of such sets can be non-zero in this context. Other counterexamples will show that the patch counting entropy of such a set can not be computed along a limit and even be infinite in this setting.
