Lattes Maps and Combinatorial Expansion.

Lattes Maps;Thurston Maps;Sphere;Postcritically Finite;Mathematics;Science;Mathematics

Yin, QianTappenden, James P. ;

University of Michigan

关键词: Lattes Maps;    Thurston Maps;    Sphere;    Postcritically Finite;    Mathematics;    Science;    Mathematics;   

Others  :  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/86524/qyin_1.pdf?sequence=1&isAllowed=y

瑞士|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 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.