The time operator of the cusp map (Q1862367)

Time operators were studied by the author for wavelets which are age eigenfunctions shifted by dilations and for unilateral shifts arising from the Koopman operator of exact dynamical systems. The cusp map is defined from \([-1, 1]\) to \([-1, 1]\) as \(F(x) = 1 -\sqrt{| x| }.\) In this paper, the author constructs a time operator and age eigenfunctions for the cusp map.