Dynamical Systems seminar - The convergence of integer continued fractions

Speaker: Margaret Stanier (Faculty of STEM, The Open University)

Abstract: Fundamental to the theory of continued fractions is the fact that every infinite continued fraction with positive coefficients converges. This is not the case, however, if the coefficients are not necessarily positive. We use a geometric representation of an integer continued fraction to find a simple test which determines whether such a fraction converges or diverges. This is joint work with Ian Short.