Publications (9)
New Normal Forms For Degree Three Polynomials and Rational Functions
Heidi Benham, Alexander Galarraga, Benjamin Hutz +3
When studying families in the moduli space of dynamical systems, choosing an appropriate representative function for a conjugacy class can be a delicate task. The most delicate que…
Endomorphisms of Bounded Height and Resultant
Brian Stout, Adam Towsley
Let K be an algebraic number field. For a degree d rational morphism of projective n-space defined over K let R denote its minimal resultant ideal. For a fixed height function on t…
Misiurewicz Points for Polynomial Maps and Transversality
Benjamin Hutz, Adam Towsley
The behavior under iteration of the critical points of polynomial maps plays an essential role in understanding its dynamics. We study the special case where the forward orbits of…
Permutation polynomials: iteration of shift and inversion maps over finite fields
Anna Chlopecki, Juliano Levier-Gomes, Wayne Peng +2
We show that all permutations in can be generated by affine unicritical polynomials. We use the group structure to compute the cycle structure of permuta…
Newton's Method Over Global Height Fields
Xander Faber, Adam Towsley
Newton's method is used to approximate roots of complex valued functions f by creating a sequence of points that converges to a root of f in the usual topology. For any field K equ…
Integrality and Thurston Rigidity for Bicritical PCF Polynomials
Heidi Benham, Alexander Galarraga, Benjamin Hutz +3
We give an algebraic proof of an important consequence of Thurston rigidity for bicritical PCF polynomials with periodic critical points under certain mild assumptions. The key res…
Evidence for the Dynamical Brauer-Manin Criterion
Ekaterina Amerik, Par Kurlberg, Khoa Nguyen +3
Let f:X->X be a morphism of a variety over a number field K. We consider local conditions and a "Bruaer-Manin" condition, defined by Hsia and Silverman, for the orbit of a point P…
Correlation Angles and Inner Products: Application to a Problem from Physics
David H. Douglass, Jonathan Pakianathan, Adam Towsley
Covariance is used as an inner product on a formal vector space built on n random variables to define measures of correlation Md across a set of vectors in a d-dimensional space. F…
A Hasse Principle for Periodic Points
Adam Towsley
Let be a global field, let $\vp \in \Fx$ be a rational map of degree at least 2, and let $\a \in F$. We say that $\a $ is periodic if $\vpn (\a) = \a$ for some . A Ha…