An element of a group is \emph{ reversible} if it is conjugate to its own inverse, and it is \emph{ 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.
Categories: math.GR math.DS