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.
Mathematics Subject Classification (2000)
Primary 37E05 57S05 Secondary 57S25
Reversible involution piecewise linear
This is a preview of subscription content, log in to check access.
Arnol’d V.I., Sevryuk M.B.: Oscillations and bifurcations in reversible systems. Nonlinear Phenom. Plasma Phys. Hydrodyn. 3, 265–334 (1986)Google Scholar
Birkhoff G.D.: The restricted problem of three bodies. Rend. Circ. Mat. Palermo 39, 265–334 (1915)CrossRefGoogle Scholar
Brin M.G., Squier C.C.: Presentations, conjugacy, roots, and centralizers in groups of piecewise linear homeomorphisms of the real line. Comm. Algebra 29(10), 4557–4596 (2001)MATHCrossRefMathSciNetGoogle Scholar
McCarthy P.J., Stephenson W.: The classification of the conjugacy classes of the full group of homeomorphisms of an open interval and the general solution of certain functional equations. Proc. Lond. Math. Soc. 51(3), 95–112 (1985)MATHCrossRefMathSciNetGoogle Scholar
O’Farrell A.G.: Conjugacy, involutions, and reversibility for real homeomorphisms. Irish Math. Soc. Bull. 54, 41–52 (2004)MATHMathSciNetGoogle Scholar
Young S.: The representation of homeomorphisms on the interval as finite compositions of involutions. Proc. Am. Math. Soc. 121, 605–610 (1994)MATHCrossRefGoogle Scholar