Reversibility in the groups of PL^+(S^1) and PL(S^1)
Khadija Ben Rejeb, Habib Marzougui
TL;DR
This paper characterizes reversible elements within the groups of order-preserving and general piecewise linear homeomorphisms of the circle, providing a detailed understanding of their conjugacy properties.
Contribution
It offers a complete characterization of reversible elements in both PL+(S1) and PL(S1), advancing the understanding of their algebraic structure.
Findings
Reversible elements are explicitly characterized in PL+(S1).
Reversible elements are explicitly characterized in PL(S1).
The results clarify conjugacy relations in these groups.
Abstract
Let PL+(S1) be the group of order preserving piecewise linear homeomorphisms of the circle. An element in PL+(S1) is called reversible in PL+(S1) if it is conjugate to its inverse in PL+(S1). We characterize the reversible elements in PL+(S1). We also perform a sim- ilar characterisation in the full group PL(S1) of piecewise linear home- omorphisms of the circle.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Topics in Algebra · Advanced Differential Equations and Dynamical Systems