Arithmetic dynamics is the study of number theoretic properties of dynamical systems. A
relatively new field, it draws inspiration partly from dynamical analogues of theorems and …

Abstract Motivated by Lang–Vojta's conjecture, we show that the set of dominant rational self-
maps of an algebraic variety over a number field with only finitely many rational points in any …

In this paper, we study arithmetic dynamics in arbitrary characteristic, in particular in positive
characteristic. Applying the arithmetic degree and canonical height in positive characteristic …

arXiv:2311.16369v1 [math.AG] 27 Nov 2023 Page 1 arXiv:2311.16369v1 [math.AG] 27 Nov
2023 ADVANCES IN THE EQUIVARIANT MINIMAL MODEL PROGRAM AND THEIR …

We give examples of birational selfmaps of P d, d⩾ 3 P^d,d\geqslant3, whose dynamical
degree is a transcendental number. This contradicts a conjecture by Bellon and Viallet. The …

Let $ f $ be a dominant endomorphism of a smooth projective surface $ X $ over an
algebraically closed field $\mathbf {k} $ of characteristic $0 $. We prove that if there is no …

We show that if the automorphism group of a projective variety is torsion, then it is finite.
Motivated by Lang's conjecture on rational points of hyperbolic varieties, we use this to …

For a surjective self-morphism on a projective variety defined over a number field, we study
the preimages question, which asks if the set of rational points on the iterated preimages of …

For a complex polynomial $ D (t) $ of even degree, one may define the continued fraction of
$\sqrt {D (t)} $. This was found relevant already by Abel in 1826, and then by Chebyshev …

There are three aims of this note. The first one is to report some advances around the
dynamical Mordell-Lang (= DML) conjecture. Second, we generalize some known results …