The quasiperiod for the continued fraction of e ~ 2.718 can be written as the three polynomials {1,2k,1}, "modulo rotation and translation", e.g. {2k-2,1,1}. It can also be "inflated" by a factor of 2 or 3 or ..., e.g {1,4k,1,1,4k+2,1} or {1,6k,1,1,6k+2,1,1,6k+4,1} or ... . If I heard him right, Julian has proved that given the Hurwitz # x :={P0(k),P1(k),...}, there is an inflation factor Δ ≤ (ad-bc)^4 such that the quasiperiod of y:=(ax+b)/(cx+d) can be written by inflating x by Δ and then replacing each polynomial Pi with an even number of constant polynomials, followed by a polynomial with the same degree as Pi. In particular, linear terms cannot arise from nonlinear terms. The resulting CF of y may often be "deflated" to have a shorter quasiperiod than x. --rwg One use of this theorem is to detect the possibility or impossibility of finding a homographic transformation shortening a long quasiperiod. For some reason, Julian disavows calling this a "structure theorem". It can probably be extended to cover exponential (e.g.) as well as polynomial terms.