The Dynamical Mordell-Lang Conjecture is an analogue of the classical Mordell-Lang
conjecture in the context of arithmetic dynamics. It predicts the behavior of the orbit of a point …

We study algebraic dynamical systems (and, more generally, σ-varieties) Φ:A^n_C→A^n_C
given by coordinatewise univariate polynomials by refining an old theorem of Ritt on …

We prove the equivalence of dynamical stability, preperiodicity, and canonical height 0, for
algebraic families of rational maps ft: ℙ 1 (ℂ)→ ℙ 1 (ℂ), parameterized by t in a …

We prove Zhang's dynamical Manin–Mumford conjecture and dynamical Bogomolov
conjecture for dominant endomorphisms of. We use the equidistribution theorem for points of …

We study the functional equation $ A\circ X= X\circ B $, where $ A, $$ B $, and $ X $ are
polynomials over $\mathbb C $. Using previous results of the author about polynomials …

C for which there is a field automorphism σ: C→ C with Φ (X)= Xσ. As consequences, we
deduce a variant of a conjecture of Zhang on the existence of rational points with Zariski …

Abstract According to Medvedev and Scanlon [14], a polynomial f (x)∈ Q¯[x] of degree d≥ 2
is called disintegrated if it is not conjugate to xd or to±C d (x)(where C d is the Chebyshev …

Abstract Let A 1, A 2∈ C (z) be rational functions of degree at least two that are neither
Lattès maps nor conjugate to z±n or±T n. We describe invariant, periodic, and preperiodic …

These notes present recent progress on a conjecture about the dynamics of rational maps
on ℙ1 (ℂ), connecting critical orbit relations and the structure of the bifurcation locus to the …

There are two fundamental problems motivated by Silverman's conversations over the years
concerning the nature of the exact values of canonical heights of f (z)∈ Q¯(z) with d:= deg …