On the dynamics of G-solenoids. Applications to Delone sets
On the dynamics of G-solenoids. Applications to Delone sets
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关于 G 螺线管的动力学。
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
J. Gambaudo
中科院分区：
文献类型：
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作者：
R. Benedetti;J. Gambaudo
一个G-螺线管是一个层空间，它的叶是一个单一的李群G的副本，它的断面是完全不连通的集合。它继承了一个G作用，可以被认为是一个动力系统。Cantor集上的自由Z-d-作用以及一大类平铺空间都具有这样的G-d-结构。对于一大类李群，我们证明了G-螺线管可以被视为以G为模型的分支流形的投影极限。这使我们能够给出一个拓扑描述的横向不变的措施与G-螺线管在一个正锥的投影极限的dim（G）-同调群的这些分支流形。特别是，我们表现出一个简单的标准意味着唯一的遍历性。特别注意的情况下，李群G是一组仿射方向保持等距的欧氏空间或其子组的翻译。
A G-solenoid is a laminated space whose leaves are copies of a single Lie group G and whose transversals are totally disconnected sets. It inherits a G-action and can be considered as a dynamical system. Free Z d -actions on the Cantor set as well as a large class of tiling spaces possess such a structure of G-solenoids. For a large class of Lie groups, we show that a G-solenoid can be seen as a projective limit of branched manifolds modeled on G. This allows us to give a topological description of the transverse invariant measures associated with a G-solenoid in terms of a positive cone in the projective limit of the dim(G)-homology groups of these branched manifolds. In particular, we exhibit a simple criterion implying unique ergodicity. Particular attention is paid to the case when the Lie group G is the group of affine orientation-preserving isometries of the Euclidean space or its subgroup of translations.