Current trends and open problems in arithmetic dynamics
R Benedetto, P Ingram, R Jones, M Manes… - Bulletin of the American …, 2019 - ams.org
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 …
relatively new field, it draws inspiration partly from dynamical analogues of theorems and …
[图书][B] Point-Counting and the Zilber–Pink Conjecture
J Pila - 2022 - books.google.com
Point-counting results for sets in real Euclidean space have found remarkable applications
to diophantine geometry, enabling significant progress on the André–Oort and Zilber–Pink …
to diophantine geometry, enabling significant progress on the André–Oort and Zilber–Pink …
Preperiodic points for families of rational maps
D Ghioca, LC Hsia, TJ Tucker - Proceedings of the London …, 2015 - academic.oup.com
Let be a smooth curve defined over, let and let be an algebraic family of rational maps
indexed by all. We study whether there exist infinitely many such that both and are …
indexed by all. We study whether there exist infinitely many such that both and are …
A dynamical variant of the André-Oort conjecture
D Ghioca, H Ye - International Mathematics Research Notices, 2018 - academic.oup.com
In the moduli space of degree polynomials, special subvarieties are those cut out by critical
orbit relations, and then special points are the post-critically finite polynomials. It was …
orbit relations, and then special points are the post-critically finite polynomials. It was …
On the dynamical Bogomolov conjecture for families of split rational maps
NM Mavraki, H Schmidt - arXiv preprint arXiv:2201.10455, 2022 - arxiv.org
We prove that Zhang's dynamical Bogomolov conjecture holds uniformly along $1 $-
parameter families of rational split maps and curves. This provides dynamical analogues of …
parameter families of rational split maps and curves. This provides dynamical analogues of …
The dynamical André–Oort conjecture: unicritical polynomials
D Ghioca, H Krieger, KD Nguyen, H Ye - 2017 - projecteuclid.org
We establish equidistribution with respect to the bifurcation measure of postcritically finite
(PCF) maps in any one-dimensional algebraic family of unicritical polynomials. Using this …
(PCF) maps in any one-dimensional algebraic family of unicritical polynomials. Using this …
Quasi-adelic measures and equidistribution on
NM Mavraki, H Ye - Ergodic Theory and Dynamical Systems, 2023 - cambridge.org
Baker and Rumely, Favre, Rivera, and Letelier, and Chambert-Loir proved an important
arithmetic equidistribution theorem for points of small height associated to an adelic …
arithmetic equidistribution theorem for points of small height associated to an adelic …
The geometry of preperiodic points in families of maps on
L DeMarco, NM Mavraki - arXiv preprint arXiv:2407.10894, 2024 - arxiv.org
We study the dynamics of algebraic families of maps on $\mathbb {P}^ N $, over the field
$\mathbb {C} $ of complex numbers, and the geometry of their preperiodic points. The goal …
$\mathbb {C} $ of complex numbers, and the geometry of their preperiodic points. The goal …
Julia sets and bifurcation loci
T Gauthier, G Vigny - arXiv preprint arXiv:2411.16178, 2024 - arxiv.org
We prove that several dynamically defined fractals in $\mathbb {C} $ and $\mathbb {C}^ 2$
which arise from different type of polynomial dynamical systems can not be the same …
which arise from different type of polynomial dynamical systems can not be the same …