8 papers
Unlikely intersections in families of polynomial skew products
Chatchai Noytaptim, Xiao Zhong
Motivated by the study of unlikely intersection in the moduli space of rational maps, we initiate our investigation on algebraic dynamics for families of regular polynomial skew pr…
On relative fields of definition for log pairs, Vojta's height inequalities and asymptotic coordinate size dynamics
Nathan Grieve, Chatchai Noytaptim
We build on the perspective of the works \cite{Grieve:Noytaptim:fwd:orbits}, \cite{Matsuzawa:2023}, \cite{Grieve:qualitative:subspace}, \cite{Grieve:chow:approx}, \cite{Grieve:Divi…
Towards Common Zeros of Iterated Morphisms
Chatchai Noytaptim, Xiao Zhong
Recently, the authors have proved the finiteness of common zeros of two iterated rational maps under some compositional independence assumptions. In this article, we advance toward…
On non-Zariski density of -integral points in forward orbits and the Subspace Theorem
Nathan Grieve, Chatchai Noytaptim
Working over a base number field $\KK$, we study the attractive question of Zariski non-density for -integral points in the forward -orbit of a rational…
Totally real algebraic numbers in generalized Mandelbrot set
Kevin G. Hare, Chatchai Noytaptim
In this article, we study some potential theoretical and topological aspects of the generalized Mandelbrot set introduced by Baker and DeMarco. For real, we study the set of al…
A finiteness result for common zeros of iterates of rational maps
Chatchai Noytaptim, Xiao Zhong
Answering a question asked by Hsia and Tucker in their paper on the finiteness of greatest common divisors of iterates of polynomials, we prove that if are…
Preperiodic points with local rationality conditions in the quadratic unicritical family
Chatchai Noytaptim
For rational numbers , we present a trichotomy of the set of totally real (totally -adic, respectively) preperiodic points for maps in the quadratic unicritical family $f_c(x…
Totally real algebraic integers in short intervals, Jacobi polynomials, and unicritical families in arithmetic dynamics
Chatchai Noytaptim, Clayton Petsche
We classify all post-critically finite unicritical polynomials defined over the maximal totally real algebraic extension of . Two auxiliary results used in the proof o…