scholarly journals Reductions modulo primes of systems of polynomial equations and algebraic dynamical systems

2018 ◽  
Vol 371 (2) ◽  
pp. 1169-1198 ◽  
Author(s):  
Carlos D’Andrea ◽  
Alina Ostafe ◽  
Igor E. Shparlinski ◽  
Martín Sombra
Keyword(s):  
Dynamical Systems ◽  
Polynomial Equations ◽  
Algebraic Dynamical Systems ◽  
Systems Of Polynomial Equations

Construction of systems of polynomial equations with exact p-Divisibility via the covering method

2014 ◽  
Vol 13 (06) ◽  
pp. 1450013 ◽  
Author(s):  
Francis N. Castro ◽  
Ivelisse M. Rubio
Keyword(s):  
Exponential Sums ◽  
Polynomial Equations ◽  
Prime Field ◽  
Elementary Method ◽  
Covering Method ◽  
Systems Of Polynomial Equations

We present an elementary method to compute the exact p-divisibility of exponential sums of systems of polynomial equations over the prime field. Our results extend results by Carlitz and provide concrete and simple conditions to construct families of polynomial equations that are solvable over the prime field.

scholarly journals Linear Network Codes and Systems of Polynomial Equations

2008 ◽  
Vol 54 (5) ◽  
pp. 2303-2316 ◽  
Author(s):  
Randall Dougherty ◽  
Chris Freiling ◽  
Kenneth Zeger
Keyword(s):  
Polynomial Equations ◽  
Linear Network ◽  
Network Codes ◽  
Systems Of Polynomial Equations

scholarly journals Bivariate systems of polynomial equations with roots of high multiplicity

2021 ◽  
Author(s):  
I. Nikitin
Keyword(s):  
High Multiplicity ◽  
Polynomial Equations ◽  
Support Sets ◽  
Multiplicity Formula ◽  
System Of Polynomial Equations ◽  
Systems Of Polynomial Equations

Given a bivariate system of polynomial equations with fixed support sets [Formula: see text] it is natural to ask which multiplicities its solutions can have. We prove that there exists a system with a solution of multiplicity [Formula: see text] for all [Formula: see text] in the range [Formula: see text], where [Formula: see text] is the set of all integral vectors that shift B to a subset of [Formula: see text]. As an application, we classify all pairs [Formula: see text] such that the system supported at [Formula: see text] does not have a solution of multiplicity higher than [Formula: see text].

scholarly journals Surjunctivity and topological rigidity of algebraic dynamical systems

2017 ◽  
Vol 39 (3) ◽  
pp. 604-619 ◽  
Author(s):  
SIDDHARTHA BHATTACHARYA ◽  
TULLIO CECCHERINI-SILBERSTEIN ◽  
MICHEL COORNAERT
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Sufficient Conditions ◽  
Countable Group ◽  
Continuous Group ◽  
Continuous Map ◽  
Algebraic Dynamical Systems ◽  
Metrizable Group ◽  
Group Automorphisms

Let$X$be a compact metrizable group and let$\unicode[STIX]{x1D6E4}$be a countable group acting on$X$by continuous group automorphisms. We give sufficient conditions under which the dynamical system$(X,\unicode[STIX]{x1D6E4})$is surjunctive, i.e. every injective continuous map$\unicode[STIX]{x1D70F}:X\rightarrow X$commuting with the action of$\unicode[STIX]{x1D6E4}$is surjective.

Sur une notion d'autonomie de systèmes dynamiques, appliquée aux ensembles invariants des flots d' Anosov algébriques

1995 ◽  
Vol 15 (1) ◽  
pp. 175-207 ◽  
Author(s):  
A. Zeghib
Keyword(s):  
Dynamical Systems ◽  
Finite Volume ◽  
Algebraic Dynamical Systems ◽  
Anosov Systems ◽  
Anosov System ◽  
Autonomous Dynamical Systems

AbstractWe introduce a notion of autonomous dynamical systems which generalizes algebraic dynamical systems. We show by giving examples and by describing some properties that this generalization is not a trivial one. We apply the methods then developed to algebraic Anosov systems. We prove that a C1-submanifold of finite volume, which is invariant by an algebraic Anosov system is ‘essentially’ algebraic.

Sign in / Sign up

Export Citation Format

Share Document