Glasner and Megrelishvili [Trans. Amer. Math. Soc. 375 (2022), pp. 4513–4548] proved that every continuous action of a topological group G on a dendrite X is tame. We produce two examples of an action on a dendrite which is not tame1, answering a question they raised. We then show that actions on dendrites have β-rank at most 2 and produce examples of tame metric dynamical systems of β-rank α for any α < ω1, answering another question of Glasner and Megrelishvili.
Codenotti, A. (2025). SOME EXAMPLES OF TAME DYNAMICAL SYSTEMS ANSWERING QUESTIONS OF GLASNER AND MEGRELISHVILI. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 153(6), 2433-2449 [10.1090/proc/16726].
SOME EXAMPLES OF TAME DYNAMICAL SYSTEMS ANSWERING QUESTIONS OF GLASNER AND MEGRELISHVILI
Codenotti A.
2025
Abstract
Glasner and Megrelishvili [Trans. Amer. Math. Soc. 375 (2022), pp. 4513–4548] proved that every continuous action of a topological group G on a dendrite X is tame. We produce two examples of an action on a dendrite which is not tame1, answering a question they raised. We then show that actions on dendrites have β-rank at most 2 and produce examples of tame metric dynamical systems of β-rank α for any α < ω1, answering another question of Glasner and Megrelishvili.| File | Dimensione | Formato | |
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