This book is designed to provide a path for the reader into an amalgamation oftwo venerable
areas ofmathematics, Dynamical Systems and Number Theory. Many of the motivating …

The purpose of this book is to develop the foundations of potential theory and rational
dynamics on the Berkovich projective line over an arbitrary complete, algebraically closed …

Consider following generalized Bogomolov conjecture: Let A be an abelian variety over Q,
h: A (Q)→ R a Néron-Tate height function with respect to an ample and symmetric line …

arxiv:2311.15489v1 [math.AG] 27 Nov 2023 Page 1 arxiv:2311.15489v1 [math.AG] 27 Nov 2023
RECENT ADVANCES ON KAWAGUCHI-SILVERMAN CONJECTURE YOHSUKE MATSUZAWA …

Let φ: PN→ PN be a morphism of degree d≥ 2 defined over a number field K.
Independently, DG Northcott [17] and DJ Lewis [9] have shown that φ has only finitely many …

Complex dynamic system is a subject to study iterations on P1 or PN with respect to complex
topology. It originated from the study of Newton method and the three body problem in the …

It has been conjectured that for $ N $ sufficiently large, there are no quadratic polynomials in
$\bold Q [z] $ with rational periodic points of period $ N $. Morton proved there were none …

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 …

Étant donné une fonction rationnelle de degré au moins 2 défini sur un corps de nombres k,
nous montrons que pour chaque place v de k, il existe une seule mesure μ ϕ, v sur l'espace …

We introduce a general strategy for proving quantitative and uniform bounds on the number
of common points of height zero for a pair of inequivalent height functions on P^1(Q). We …