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Girth Alternative for subgroups of $PL_o(I)$

Part of: Low-dimensional dynamical systems Smooth dynamical systems: general theory

Published online by Cambridge University Press:  09 May 2024

Azer Akhmedov
Azer Akhmedov*
Affiliation:
Department of Mathematics, North Dakota State University, Fargo, ND, 58108, USA
*
Email: azer.akhmedov@ndsu.edu
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Abstract

We prove the Girth Alternative for finitely generated subgroups of $PL_o(I)$. We also prove that a finitely generated subgroup of Homeo$_{+}(I)$ which is sufficiently rich with hyperbolic-like elements has infinite girth.

MSC classification

Primary: 37E05: Maps of the interval (piecewise continuous, continuous, smooth)
Secondary: 37C85: Dynamics of group actions other than ${bf Z}$ and ${bf R}$, and foliations

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 67 , Issue 1 , January 2025 , pp. 1 - 10
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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