Dynamics in Thompson's Group F
James Belk, Francesco Matucci
TL;DR
This paper explores the dynamics of Thompson's group F by linking strand diagrams to piecewise-linear functions, and introduces a Mather-type invariant to characterize conjugacy of one-bump functions.
Contribution
It establishes an explicit connection between strand diagrams and functions in F, and introduces a new invariant for conjugacy analysis.
Findings
Relationship between strand diagrams and piecewise-linear functions
Conjugacy of one-bump functions characterized by a Mather-type invariant
Enhanced understanding of dynamics in Thompson's group F
Abstract
We describe an explicit relationship between strand diagrams and piecewise-linear functions for elements of Thompson's group F. Using this correspondence, we investigate the dynamics of elements of F, and we show that conjugacy of one-bump functions can be described by a Mather-type invariant.
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Taxonomy
TopicsGeometric and Algebraic Topology · Mathematical Dynamics and Fractals · Homotopy and Cohomology in Algebraic Topology