Topological dynamics of kaleidoscopic groups

Kaleidoscopic groups are a class of permutation recently introduced by Duchesne, Monod, and Wesolek. Starting with group Γ, the kaleidoscopic construction produces another K(Γ) which acts on Ważewski dendrite (a densely branching tree-like compact space). In this paper, we study how topological dynamics can be expressed in terms one when Γ is transitive. By proving Ramsey theorem for decorated rooted trees, show that universal minimal flow (UMF) metrizable iff oligomorphic UMF metrizable. More generally, give concrete calculations, an appropriate model-theoretic framework, point stabilizer Γc has comeager orbit. Our results also large examples non-metrizable UMFs These extend previous work Kwiatkowska Duchesne about full homeomorphism groups.