Gill, Nick and Short, Ian
Reversible maps and composites of involutions in groups of piecewise linear homeomorphisms of the real line.
Aequationes Mathematicae, 79(1-2) pp. 23–37.
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An element of a group is reversible if it is conjugate to its own inverse, and it is strongly reversible if it is conjugate to its inverse by an involution. A group element is strongly reversible if and only if it can be expressed as a composite of two involutions. In this paper the reversible maps, the strongly reversible maps, and those maps that can be expressed as a composite of involutions are determined in certain groups of piecewise linear homeomorphisms of the real line.
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