Dynamics of a family of piecewise-linear area-preserving plane maps III. Cantor set spectra

Jeffrey C. Lagarias, Eric Rains

This paper studies the behavior under iteration of the maps T_{ab}(x,y) = (F_{ab}(x)- y, x) of the plane R^2, in which F_{ab}(x)= ax if x>0 and bx if x<0. These maps are area-prese…