Invariant Measures for Reducible Generalized Bratteli Diagrams

In 2010, Bezuglyi, Kwiatkowski, Medynets, and Solomyak [10] found a complete description of the set of probability ergodic tail invariant measures on the path space of a standard (classical) stationary reducible Bratteli diagram. It was shown that every distinguished eigenvalue for the incidence mat...

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Збережено в:
Бібліографічні деталі
Дата:2024
Автори: Bezuglyi, Sergey, Karpel, Olena, Kwiatkowski, Jan
Формат: Стаття
Мова:English
Опубліковано: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України 2024
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Онлайн доступ:https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1050
Теги: Додати тег
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Назва журналу:Journal of Mathematical Physics, Analysis, Geometry

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Journal of Mathematical Physics, Analysis, Geometry
Опис
Резюме:In 2010, Bezuglyi, Kwiatkowski, Medynets, and Solomyak [10] found a complete description of the set of probability ergodic tail invariant measures on the path space of a standard (classical) stationary reducible Bratteli diagram. It was shown that every distinguished eigenvalue for the incidence matrix determines a probability ergodic invariant measure. In this paper, we show that this result does not hold for stationary reducible generalized Bratteli diagrams. We consider classes of stationary and non-stationary reducible generalized Bratteli diagrams with infinitely many simple standard subdiagrams, in particular, with infinitely many odometers as subdiagrams. We characterize the sets of all probability ergodic invariant measures for such diagrams and study partial orders under which the diagrams can support a Vershik homeomorphism. Mathematical Subject Classification 2020: 37A05, 37B05, 37A40, 54H05,05C60