We study the involution of the real line, induced by Dyer's outer automorphism of PGL(2,Z). It is continuous at irrationals with jump discontinuities at rationals. We prove that its derivative exists almost everywhere and vanishes almost everywhere.
Involution, PGL, projective general linear group, continued fraction, derivative, discontinuity
ULUDAĞ, ABDURRAHMAN MUHAMMED and AYRAL, HAKAN
"An involution of reals, discontinuous on rationals, and whose derivative vanishes a.e.,"
Turkish Journal of Mathematics: Vol. 43:
3, Article 49.
Available at: https://journals.tubitak.gov.tr/math/vol43/iss3/49