Výsledky vyhledávání - "Clayton Petsche"

Totally $T$-adic functions of small height

Publikováno v: Rendiconti Lincei - Matematica e Applicazioni. 31:699-732

Let $\mathbb{F}_q(T)$ be the field of rational functions in one variable over a finite field. We introduce the notion of a totally $T$-adic function: one that is algebraic over $\mathbb{F}_q(T)$ and whose minimal polynomial splits completely over the

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https://doi.org/10.4171/rlm/911

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Abelian extensions in dynamical Galois theory

Autor: Jesse Andrews, Clayton Petsche

Publikováno v: Algebra Number Theory 14, no. 7 (2020), 1981-1999

We propose a conjectural characterization of when the dynamical Galois group associated to a polynomial is abelian, and we prove our conjecture in several cases, including the stable quadratic case over [math] . In the postcritically infinite case, t

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https://doi.org/10.2140/ant.2020.14.1981

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Attractors associated to a family of hyperbolic -adic plane automorphisms

Autor: Clayton Petsche

Publikováno v: Ergodic Theory and Dynamical Systems. 41:1867-1882

We consider a certain two-parameter family of automorphisms of the affine plane over a complete, locally compact non-Archimedean field. Each of these automorphisms admits a chaotic attractor on which it is topologically conjugate to a full two-sided

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https://doi.org/10.1017/etds.2020.20

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A dynamical construction of small totally p-adic algebraic numbers

Autor: Clayton Petsche, Emerald Stacy

Publikováno v: Journal of Number Theory. 202:27-36

We give a dynamical construction of an infinite sequence of distinct totally p-adic algebraic numbers whose Weil heights tend to the limit log ⁡ p p − 1 , thus giving a new proof of a result of Bombieri-Zannier. The proof is essentially equivalen

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https://doi.org/10.1016/j.jnt.2019.01.021

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Energy integrals and small points for the Arakelov height

Autor: Igor E. Pritsker, Clayton Petsche, Paul Fili

Publikováno v: Archiv der Mathematik. 109:441-454

We study small points for the Arakelov height on the projective line. First, we identify the smallest positive value taken by the Arakelov height, and we characterize all cases of equality. Next we solve several archimedean energy minimization proble

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https://doi.org/10.1007/s00013-017-1080-x

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A $p$-adic Perron–Frobenius theorem

Autor: Clayton Petsche, Patrick Dynes, Robert Costa

Publikováno v: Acta Arithmetica. :1-14

We prove a result for square matrices over the p-adic numbers akin to the Perron-Frobenius Theorem for square matrices over the real numbers. In particular, we show that if a square n n matrix A has all entries p-adically close to 1, then this matrix

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https://doi.org/10.4064/aa8285-4-2016

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Non-Archimedean Hénon maps, attractors, and horseshoes

Autor: Clayton Petsche, David DeMark, Kenneth Allen

Publikováno v: Research in Number Theory. 4

We study the dynamics of the Henon map defined over complete, locally compact non-Archimedean fields of odd residue characteristic. We establish basic properties of its one-sided and two-sided filled Julia sets, and we determine, for each Henon map,

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https://doi.org/10.1007/s40993-018-0105-2

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A Dirichlet approximation theorem for group actions

Autor: Jeffrey D. Vaaler, Clayton Petsche

Publikováno v: Funct. Approx. Comment. Math. 60, no. 2 (2019), 263-275

If $G$ is a compact group acting continuously on a compact metric space $(X, m)$, we prove two results that generalize Dirichlet's classical theorem on Diophantine approximation. If $G$ is a noncommutative compact group of isometries, we obtain a non

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On quadratic rational maps with prescribed good reduction

Autor: Brian Stout, Clayton Petsche

Publikováno v: Proceedings of the American Mathematical Society. 143:1145-1158

Given a number field $K$ and a finite set $S$ of places of $K$, the first main result of this paper shows that the quadratic rational maps $\phi:{\mathbb P}^1\to{\mathbb P}^1$ defined over $K$ which have good reduction at all places outside $S$ compr

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https://doi.org/10.1090/s0002-9939-2014-12291-x

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A dynamical pairing between two rational maps

Autor: Thomas J. Tucker, Lucien Szpiro, Clayton Petsche

Publikováno v: Transactions of the American Mathematical Society. 364:1687-1710

This is the publisher’s final pdf. The published article is copyrighted by American Mathematical Society and can be found at: http://www.ams.org/home/page.

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https://doi.org/10.1090/s0002-9947-2011-05350-x

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