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Invariant Subsets and Invariant Measures for Irreducible Actions on Zero‐Dimensional Groups
Author(s) -
Einsiedler Manfred
Publication year - 2004
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609303003023
Subject(s) - mathematics , invariant (physics) , pure mathematics , zero (linguistics) , invariant polynomial , mathematical analysis , mathematical physics , philosophy , linguistics , matrix polynomial , polynomial
Algebraic higher‐rank actions on connected groups are often remarkably rigid in their topological and measurable structure. In contrast to this, the author of this paper constructs uncountably many closed invariant sets and uncountably many invariant measures with positive entropy for irreducible algebraic Z d ‐actions on zero‐dimensional groups. 2000 Mathematics Subject Classification 37A45 (primary), 37B50, 37A35, 37B40 (secondary).