Xiao Zhong, University of Waterloo
Topics in Arithmetic Dynamics
This thesis studies several problems in arithmetic dynamics, focusing on preimages of invariant subvarieties,common zeros of iterates of rational functions, and periodic curves for polynomial endomorphisms. Weinvestigate stabilization phenomena for rational points in backward orbits and develop dynamical cancellationresults for semigroups of polynomials. We also prove a finiteness theorem for common zeros of iterates ofcompositionally independent rational functions, answering a question of Hsia and Tucker. Finally, we studypolynomial endomorphisms of the projective plane with many periodic curves, showing that families containinga Zariski dense set of periodic curves must be invariant under an iterate, and we classify maps admittinginfinitely many periodic curves of bounded degree.
MC 5479