Displaying similar documents to “A criterion for potentially good reduction in nonarchimedean dynamics”

A dynamical Shafarevich theorem for twists of rational morphisms

Brian Justin Stout (2014)

Acta Arithmetica


Let K denote a number field, S a finite set of places of K, and ϕ: ℙⁿ → ℙⁿ a rational morphism defined over K. The main result of this paper states that there are only finitely many twists of ϕ defined over K which have good reduction at all places outside S. This answers a question of Silverman in the affirmative.

On the C⁰-closing lemma

Anna A. Kwiecińska (1996)

Annales Polonici Mathematici


A proof of the C⁰-closing lemma for noninvertible discrete dynamical systems and its extension to the noncompact case are presented.

On Computer-Assisted Proving The Existence Of Periodic And Bounded Orbits

Roman Srzednicki (2015)

Annales Mathematicae Silesianae


We announce a new result on determining the Conley index of the Poincaré map for a time-periodic non-autonomous ordinary differential equation. The index is computed using some singular cycles related to an index pair of a small-step discretization of the equation. We indicate how the result can be applied to computer-assisted proofs of the existence of bounded and periodic solutions. We provide also some comments on computer-assisted proving in dynamics.

Niven’s Theorem

Artur Korniłowicz, Adam Naumowicz (2016)

Formalized Mathematics


This article formalizes the proof of Niven’s theorem [12] which states that if x/π and sin(x) are both rational, then the sine takes values 0, ±1/2, and ±1. The main part of the formalization follows the informal proof presented at Pr∞fWiki (https://proofwiki.org/wiki/Niven’s_Theorem#Source_of_Name). For this proof, we have also formalized the rational and integral root theorems setting constraints on solutions of polynomial equations with integer coefficients [8, 9].

Heights of varieties in multiprojective spaces and arithmetic Nullstellensätze

Carlos D’Andrea, Teresa Krick, Martín Sombra (2013)

Annales scientifiques de l'École Normale Supérieure


We present bounds for the degree and the height of the polynomials arising in some problems in effective algebraic geometry including the implicitization of rational maps and the effective Nullstellensatz over a variety. Our treatment is based on arithmetic intersection theory in products of projective spaces and extends to the arithmetic setting constructions and results due to Jelonek. A key role is played by the notion of canonical mixed height of a multiprojective variety. We study...

Dynamical systems with Newtonian type potentials

Marco Degiovanni, Fabio Giannoni, Antonio Marino (1987)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni


We study the existence of regular periodic solutions to some dynamical systems whose potential energy is negative, has only a singular point and goes to zero at iniìnity. We give sufficient conditions to the existence of periodic solutions of assigned period which do not meet the singularity.