On free semigroups of affine maps on the real line
Alexander Kolpakov, Alexey Talambutsa
TL;DR
This paper generalizes Klarner's work on free semigroups of affine maps on the real line using geometric group theory, specifically the Ping-Pong lemma, and explores the boundaries of Klarner's necessary condition for semigroup relations.
Contribution
It introduces a geometric approach to analyze free semigroups of affine maps and clarifies the conditions under which Klarner's criteria apply.
Findings
Extended Klarner's results using the Ping-Pong lemma
Identified boundaries for Klarner's necessary condition
Provided new insights into the structure of affine semigroup relations
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 within which Klarner's necessary condition for a semigroup to be related is applicable.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Geometric and Algebraic Topology · Point processes and geometric inequalities