On free semigroups of affine maps on the real line
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- by Alexander Kolpakov and Alexey Talambutsa
- Proc. Amer. Math. Soc. 150 (2022), 2301-2307
- DOI: https://doi.org/10.1090/proc/15832
- Published electronically: March 16, 2022
Abstract:
In this note we generalise some of the work of Klarner on free semigroups of affine maps acting on the real line by using a classical approach from geometric group theory (the Ping-Pong lemma). We also investigate the boundaries up to which the Klarner’s necessary condition for a semigroup to be related is applicable.References
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Bibliographic Information
- Alexander Kolpakov
- Affiliation: Institut de Mathématiques, Université de Neuchâtel, 2000 Neuchâtel, Switzerland; and Laboratory of combinatorial and geometric structures, Moscow Institute of Physics and Technology, Dolgoprudny, Russia
- MR Author ID: 774696
- Email: kolpakov.alexander@gmail.com
- Alexey Talambutsa
- Affiliation: Steklov Mathematical Institute of RAS, 8 Gubkina St., 119991 Moscow, Russia; and HSE University, 11 Pokrovsky Blvd., 109028 Moscow, Russia
- MR Author ID: 785209
- ORCID: 0000-0002-1237-9682
- Email: altal@mi-ras.ru
- Received by editor(s): May 21, 2021
- Received by editor(s) in revised form: September 1, 2021
- Published electronically: March 16, 2022
- Additional Notes: The first author was partially supported by SNSF (project no. PP00P2-170560) and Russian Federation Government (grant no. 075-15-2019-1926). The second author was partially supported by RFBR and SC RA (project no. 20-51-05010)
- Communicated by: Katrin Gelfert
- © Copyright 2022 by the authors
- Journal: Proc. Amer. Math. Soc. 150 (2022), 2301-2307
- MSC (2020): Primary 20M05
- DOI: https://doi.org/10.1090/proc/15832
- MathSciNet review: 4399250