scholarly journals A question for iterated Galois groups in arithmetic dynamics

2020 ◽  
pp. 1-17
Author(s):  
Andrew Bridy ◽  
John R. Doyle ◽  
Dragos Ghioca ◽  
Liang-Chung Hsia ◽  
Thomas J. Tucker
Keyword(s):  
Dynamical System ◽  
Galois Groups ◽  
General Question ◽  
Arithmetic Dynamics ◽  
Polynomial Maps ◽  
Special Cases ◽  
Unicritical Polynomials

Abstract We formulate a general question regarding the size of the iterated Galois groups associated with an algebraic dynamical system and then we discuss some special cases of our question. Our main result answers this question for certain split polynomial maps whose coordinates are unicritical polynomials.

scholarly journals Bounded Height in Families of Dynamical Systems

2017 ◽  
Vol 2019 (8) ◽  
pp. 2453-2482 ◽  
Author(s):  
Laura DeMarco ◽  
Dragos Ghioca ◽  
Holly Krieger ◽  
Khoa Dang Nguyen ◽  
Thomas Tucker ◽  
...  
Keyword(s):  
Dynamical Systems ◽  
General Result ◽  
Algebraic Integer ◽  
Arithmetic Dynamics ◽  
Special Case

Abstract Let $a,b\in\overline{\mathbb{Q}}$ be such that exactly one of $a$ and $b$ is an algebraic integer, and let $f_t(z):=z^2+t$ be a family of polynomials parameterized by $t\in\overline{\mathbb{Q}}$. We prove that the set of all $t\in\overline{\mathbb{Q}}$ for which there exist $m,n\geq 0$ such that $f_t^m(a)=f_t^n(b)$ has bounded height. This is a special case of a more general result supporting a new bounded height conjecture in arithmetic dynamics.

scholarly journals Monomial maps on P2 and their arithmetic dynamics

2011 ◽  
Vol 131 (12) ◽  
pp. 2409-2425
Author(s):  
Aryeh Gregor ◽  
Yu Yasufuku
Keyword(s):  
Arithmetic Dynamics

scholarly journals Uniform boundedness ofS-units in arithmetic dynamics

2015 ◽  
Vol 274 (1) ◽  
pp. 97-106 ◽  
Author(s):  
Holly Krieger ◽  
Aaron Levin ◽  
Zachary Scherr ◽  
Thomas Tucker ◽  
Yu Yasufuku ◽  
...  
Keyword(s):  
Uniform Boundedness ◽  
Arithmetic Dynamics

scholarly journals Current trends and open problems in arithmetic dynamics

2019 ◽  
Vol 56 (4) ◽  
pp. 611-685 ◽  
Author(s):  
Robert Benedetto ◽  
Patrick Ingram ◽  
Rafe Jones ◽  
Michelle Manes ◽  
Joseph H. Silverman ◽  
...  
Keyword(s):  
Arithmetic Dynamics ◽  
Open Problems ◽  
Current Trends

Zsigmondy theorem for arithmetic dynamics induced by a drinfeld module

2019 ◽  
Vol 15 (06) ◽  
pp. 1111-1125
Author(s):  
Zhengjun Zhao ◽  
Qingzhong Ji
Keyword(s):  
Prime Ideal ◽  
Function Field ◽  
Drinfeld Module ◽  
Torsion Point ◽  
Arithmetic Dynamics ◽  
Global Function ◽  
Ideal Formula ◽  
Global Function Field ◽  
The Ideal

Let [Formula: see text] be a Drinfeld [Formula: see text]-module defined over a global function field [Formula: see text] Let [Formula: see text] be a non-torsion point of [Formula: see text] with infinite [Formula: see text]-orbit. For each [Formula: see text] write the ideal [Formula: see text] as a quotient of relatively prime integral ideals. We establish an analogue of the classical Zsigmondy theorem for the ideal sequence [Formula: see text] i.e. for all but finitely many [Formula: see text] there exists a prime ideal [Formula: see text] such that [Formula: see text] and [Formula: see text] for all [Formula: see text]

scholarly journals ABC implies primitive prime divisors in arithmetic dynamics

2013 ◽  
Vol 45 (6) ◽  
pp. 1194-1208 ◽  
Author(s):  
C. Gratton ◽  
K. Nguyen ◽  
T. J. Tucker
Keyword(s):  
Arithmetic Dynamics ◽  
Prime Divisors
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