Growth and structure of equicontinuous foliated spaces (Q6616248)

Molino's description of Riemannian foliations on compact manifolds ([\textit{P. Molino}, Indag. Math. 44, 45--76 (1982; Zbl 0516.57016)]) extends to compact equicontinuous foliated spaces as developed by \textit{J. A. Álvarez López} and the author [Pac. J. Math. 280, No. 2, 257--314 (2016; Zbl 1337.57060)]. This extension is of particular interest when the leaves are dense and the pseudogroup exhibits strong quasi-analytic behaviour. It leads to the establishment of an association with a structural local group within such a foliated space. Application of this framework results in a partial generalization of Carriére and Breuillard-Gelander's results ([\textit{Y. Carrière}, Comment. Math. Helv. 63, No. 1, 1--20 (1988; Zbl 0661.53022)], [\textit{E. Breuillard} and \textit{T. Gelander}, Ann. Math. (2) 166, No. 2, 427--474 (2007; Zbl 1149.20039)]) creating a connection between the structural local group and the growth of leaves. Illustrative examples and a scenario with zero topological codimension are provided. In this context, instances of weak solenoids embodying this characteristic have been previously established in [\textit{J. Dyer} et al., Pac. J. Math. 289, No. 1, 91--151 (2017; Zbl 1476.57052)].\N\NFor the entire collection see [Zbl 1532.53004].