Realizations of rotations on an indecomposable compact monothetic group |
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Authors: | Daniel Maier |
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Institution: | 1. +49 (0)7071 29 78568+49 (0)7071 29 5173;2. University of Tübingen, Germany |
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Abstract: | By the classical Halmos‐von Neumann theorem, each compact monothetic group corresponds to an ergodic dynamical system with discrete spectrum. For such groups we prove two results. We first construct a compact monothetic group which does not split into a direct product of a connected and a totally disconnected compact monothetic group. Then we present a measure preserving dynamical system on the unit square being isomorphic to a rotation on this indecomposable group. |
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Keywords: | Halmos‐von Neumann theorem indecomposable compact monothetic group 35K55 35K65 |
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