Lattes Maps and Combinatorial Expansion.

[摘要] A Lattes map f : C → C is a rational map that is obtained from a finite quotient ofa conformal torus endomorphism. In this thesis, we give a characterization of Lattesmaps by their combinatorial expansion behavior. More specifically, to any Thurstonmaps, which are branched covering maps over the 2-sphere with finite post-criticalsets, there are natural cell-decompositions of the 2-sphere induced by the dynamicsfollowing Bonk and Meyer. We show that these cell decompositions give us a naturalGromov hyperbolic space, and we deduce new necessary and sufficient conditions fora Thurston map to be topologically conjugate to a Lattes map.

[发布机构] University of Michigan

[效力级别] Thurston Maps

[关键词] Lattes Maps;Thurston Maps;Sphere;Postcritically Finite;Mathematics;Science;Mathematics