Expansion properties for finite subdivision rules I

2015/08/03 by William J. Floyd, Floyd, William J., Walter R. Parry +3
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS

paper · pdf · doi:10.48550/arxiv.1508.00547

arxiv created 2015/08/03 · arxiv updated 2015/08/04

Abstract

Among Thurston maps (orientation-preserving, postcritically finite branched coverings of the 2-sphere to itself), those that arise as subdivision maps of a finite subdivision rule form a special family. For such maps, we investigate relationships between various notions of expansion---combinatorial, dynamical, algebraic, and coarse-geometric.

Related

• Expansion properties for finite subdivision rules II
• Algorithmic aspects of branched coverings IV/V. Expanding maps
• Levy and Thurston obstructions of finite subdivision rules
• Geometrization of postcritically finite branched coverings (revised)
• Geometrization of postcritically finite branched coverings