9 citations · 39 across the 19 of their papers we have counts for
30 papers · 1 filter
Characterizations of contracting Hurwitz bisets
Walter Parry, Kevin M. Pilgrim
A critically finite branched self-cover determines naturally three iterated function systems: one on the pure mapping class group of the sphere marked at…
Ahlfors-regular conformal dimension and energies of graph maps
Kevin M. Pilgrim, Dylan P. Thurston
For a hyperbolic rational map with connected Julia set, we give upper and lower bounds on the Ahlfors-regular conformal dimension of its Julia set from a family of energi…
On the pullback relation on curves induced by a Thurston map
Kevin M. Pilgrim
Via taking connected components of preimages, a Thurston map induces a pullback relation on the set of isotopy classes of curves in the complement of…
On the non-monotonicity of entropy for a class of real quadratic rational maps
Khashayar Filom, Kevin M. Pilgrim
We prove that the entropy function on the moduli space of real quadratic rational maps is not monotonic by exhibiting a continuum of disconnected level sets. This entropy behavior…
Expansion properties for finite subdivision rules II
William Floyd, Walter Parry, Kevin M. Pilgrim
We prove that every sufficiently large iterate of a Thurston map which is not doubly covered by a torus endomorphism and which does not have a Levy cycle is isotopic to the subdivi…
Bounded hyperbolic components of bicritical rational maps
Hongming Nie, Kevin M. Pilgrim
We prove that the hyperbolic components of bicritical rational maps having two distinct attracting cycles each of period at least two are bounded in the moduli space of bicritical…