Dynamics on the Moduli Space of Pointed Rational Curves

The moduli space M_{0,n} parametrizes all ways of labelling n distinct points on the Riemann sphere P^1, up to change of coordinates by Mobius transformations. Hurwitz correspondences are certain multi-valued self-maps of M_{0,n}. They arise in topology and Teichmuller theory by works of Thurston and Koch. In this thesis, we study the dynamics of Hurwitz correspondences via numerical invariants called dynamical degrees.PHDMathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/138644/1/ramadas_1.pd