Simultaneous rational periodic points of degree-2 rational maps

Official URL: https://risc01.sabanciuniv.edu/record=b2583797_(Table of contents)

In this thesis, we study the dynamical behaviour of degree two rational maps of the form kx+b/x and quadratic polynomials with rational coefficients. Assuming standard conjectures on the period length of rational periodic points of these maps, we give the possible size of the intersection of their finite orbits. In particular, we give a necessary and sufficient condition for two rational points to be periodic for infinitely many such maps.