VTechWorks staff will be away for the winter holidays starting Tuesday, December 24, 2024, through Wednesday, January 1, 2025, and will not be replying to requests during this time. Thank you for your patience, and happy holidays!

Browsing by Author "Kim, Daniel Min"

Now showing 1 - 2 of 2
  • Thumbnail Image
    Core Entropy of Finite Subdivision Rules
    Kim, Daniel Min (Virginia Tech, 2021-06-30)
    The topological entropy of the subdivision map of a finite subdivision rule restricted to the 1-skeleton of its model subdivision complex, which we call textbf{core entropy}, is examined. We consider core entropy for finite subdivision rules realizing quadratic Misiurewicz polynomials and matings of such polynomials. It is shown that for a non-restrictive class of finite subdivision rules realizing quadratic Misiurewicz polynomials, core entropy equals Thurston's core entropy. We also show that the core entropy of formal and degenerate matings of Misiurewicz polynomials is determined by Thurston's core entropy of the mated polynomials.
  • Thumbnail Image
    Nearly Euclidean Thurston Maps and the Halfspace Theorem
    Kim, Daniel Min (Virginia Tech, 2016-11-14)
    A Thurston map whose postcritical set consists of exactly four points and for which the local degree at each of its critical points is 2 is called textit{nearly Euclidean}. These maps were specified to parse Thurston's combinatorial characterization of rational functions. We determine an extension of the half-space theorem which provides an open hyperbolic half-space such that the negative reciprocal of any fixed slope value is excluded from the boundary of the half-space.