Cyclicity, hypercyclicity and randomness in self-similar groups
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| Titel: | Cyclicity, hypercyclicity and randomness in self-similar groups |
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| Autoren: | Fariña-Asategui, Jorge |
| Weitere Verfasser: | Lund University, Faculty of Science, Centre for Mathematical Sciences, Mathematics (Faculty of Sciences), Lunds universitet, Naturvetenskapliga fakulteten, Matematikcentrum, Matematik (naturvetenskapliga fakulteten), Originator |
| Quelle: | Monatshefte fur Mathematik. 207(2):275-292 |
| Schlagwörter: | Natural Sciences, Mathematical Sciences, Mathematical Analysis, Naturvetenskap, Matematik, Matematisk analys, Discrete Mathematics, Diskret matematik |
| Beschreibung: | We introduce the concept of cyclicity and hypercyclicity in self-similar groups as an analogue of cyclic and hypercyclic vectors for an operator on a Banach space. We derive a sufficient condition for cyclicity of non-finitary automorphisms in contracting discrete automata groups. In the profinite setting we prove that fractal profinite groups may be regarded as measure-preserving dynamical systems and derive a sufficient condition for the ergodicity and the mixing properties of these dynamical systems. Furthermore, we show that a Haar-random element in a super strongly fractal profinite group is hypercyclic almost surely as an application of Birkhoff’s ergodic theorem for free semigroup actions. |
| Zugangs-URL: | https://doi.org/10.1007/s00605-025-02061-6 |
| Datenbank: | SwePub |
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Nájsť tento článok vo Web of Science | Abstract: | We introduce the concept of cyclicity and hypercyclicity in self-similar groups as an analogue of cyclic and hypercyclic vectors for an operator on a Banach space. We derive a sufficient condition for cyclicity of non-finitary automorphisms in contracting discrete automata groups. In the profinite setting we prove that fractal profinite groups may be regarded as measure-preserving dynamical systems and derive a sufficient condition for the ergodicity and the mixing properties of these dynamical systems. Furthermore, we show that a Haar-random element in a super strongly fractal profinite group is hypercyclic almost surely as an application of Birkhoff’s ergodic theorem for free semigroup actions. |
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| ISSN: | 00269255 14365081 |
| DOI: | 10.1007/s00605-025-02061-6 |