5 citations · 6 across the 4 of their papers we have counts for
6 papers
Spectra of Weighted Composition Operators with Quadratic Symbols
Jessica Doctor, Timothy Hodges, Scott Kaschner +2
Previously, spectra of certain weighted composition operators on the Hardy Space were discovered under one of two hypotheses: either the compositional symbol converges under iterat…
Geometric limits of Julia sets for sums of power maps and polynomials
Micah Brame, Scott Kaschner
For maps of one complex variable, , given as the sum of a degree power map and a degree polynomial, we provide necessary and sufficient conditions that the geometric lim…
Complex Perspective for the Projective Heat Map Acting on Pentagons
Scott R. Kaschner, Roland K. W. Roeder
We place Schwartz's work on the real dynamics of the projective heat map into the complex perspective by computing its first dynamical degree and gleaning some corollaries abou…
Symmetrization of Rational Maps: Arithmetic Properties and Families of Lattès Maps of
Thomas Gauthier, Benjamin Hutz, Scott Kaschner
In this paper we study properties of endomorphisms of $\p^k$ using a symmetric product construction $(\p^1)^k/\mathfrak{S}_k \cong \p^k$. Symmetric products have been used to produ…
Geometric Limits of Julia Sets with Parameters on the Circle
Scott R. Kaschner, Reaper Romero, David Simmons
We show that the geometric limit as of the filled Julia sets for the maps does not exist for almost every on the unit…
Superstable manifolds of invariant circles and co-dimension 1 Bottcher functions
Scott R. Kaschner, Roland K. W. Roeder
We consider the situation of a dominant meromorphic self-map , where is a compact Kähler manifold of dimension . Suppose there is an embedded copy of…