Dynamical quasitilings of amenable groups

• Autorzy: Downarowicz T. , Huczek D.

Identyfikatory

DOI

10.4064/ba8128-1-2018

• Języki publikacji: EN

Abstrakty

EN

We prove that for any compact zero-dimensional metric space X on which an infinite countable amenable group G acts freely by homeomorphisms, there exists a dynamical quasitiling with good covering, continuity, Følner and dynamical properties, i.e. to every x ∈ X we can assign a quasitiling T_x of G (with all the T_x using the same, finite set of shapes) such that the tiles of T_x are disjoint, their union has arbitrarily high lower Banach density, all the shapes of T_x are large subsets of an arbitrarily large Følner set, and if we consider T_x to be an element of a shift space over a certain finite alphabet, then x ↦ T_x is a factor map.

Słowa kluczowe

EN

amenable group; dynamical system; quasitiling

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2018
• Tom: Vol. 66, no. 1
• Strony: 45--55
• Opis fizyczny: Bibliogr. 3 poz.

Twórcy

autor

Downarowicz T.

• Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

autor

Huczek D.

• Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

Bibliografia

• [DHZ] T. Downarowicz, D. Huczek and G. Zhang, Tilings of amenable groups, arXiv: 1502.02413 (2015).
• [N] I. Namioka, Følner’s conditions for amenable semi-groups, Math. Scand. 15 (1964), 18-28.
• [OW] D. S. Ornstein and B. Weiss, Entropy and isomorphism theorems for actions of amenable groups, J. Anal. Math. 48 (1987), 1-141.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).