scholarly journals Linear Dynamical Systems of Higher Genus

1994 ◽  
Vol 1 (5) ◽  
pp. 505-521
Author(s):  
V. Lomadze
Keyword(s):  
Dynamical Systems ◽  
Linear Systems ◽  
Rational Function ◽  
Function Field ◽  
Algebraic Function ◽  
Linear Dynamical Systems ◽  
Algebraic Function Field ◽  
Rational Function Field ◽  
Higher Genus

Abstract A class of linear systems which after ordinary linear systems are in a certain sense the simplest ones, is associated with every algebraic function field. From the standpoint developed in the paper ordinary linear systems are associated with the rational function field.

On Rationality of Algebraic Function Fields

1969 ◽  
Vol 12 (3) ◽  
pp. 339-341 ◽  
Author(s):  
Nobuo Nobusawa
Keyword(s):  
Rational Function ◽  
Number Field ◽  
Algebraic Number ◽  
Function Field ◽  
Algebraic Function ◽  
Algebraic Number Field ◽  
Constant Field ◽  
Algebraic Function Field ◽  
Algebraic Function Fields ◽  
Transcendental Extension

Let A be an algebraic function field with a constant field k which is an algebraic number field. For each prime p of k, we consider a local completion kp and set Ap = Ak ꕕ kp. Then we have the question:Is it true that A/k is a rational function field (i.e., A is a purely transcendental extension of k) if Ap/kp is so for every p ? In this note we shall discuss the question in a slightly different and hence easier case.

scholarly journals The differential Galois group of the rational function field

2021 ◽  
Vol 381 ◽  
pp. 107605
Author(s):  
Annette Bachmayr ◽  
David Harbater ◽  
Julia Hartmann ◽  
Michael Wibmer
Keyword(s):  
Galois Group ◽  
Rational Function ◽  
Function Field ◽  
Differential Galois Group ◽  
Rational Function Field

scholarly journals Three theorems on hierarchical decomposition of similarity linear systems

2004 ◽  
Vol 17 (2) ◽  
pp. 241-249
Author(s):  
Yuan-Wei Jing ◽  
Jun Zhao ◽  
Mile Stankovski ◽  
Georgi Dimirovski
Keyword(s):  
Dynamical Systems ◽  
Linear Systems ◽  
Hierarchical Structures ◽  
Hierarchical Decomposition ◽  
Linear Dynamical Systems ◽  
System Decomposition ◽  
Complex Linear

In this paper the problem of system decomposition of complex linear dynamical systems biy exploiting the similarity property is studied. System decompositions are sought in terms of similarity hierarchical structures. The method for constructing the transformation is derived. The conditions for such decomposition of complex linear systems are given.

MODELING LINEAR DYNAMICAL SYSTEMS BY CONTINUOUS-VALUED CELLULAR AUTOMATA

2007 ◽  
Vol 18 (05) ◽  
pp. 833-848 ◽  
Author(s):  
JUAN CARLOS SECK TUOH MORA ◽  
MANUEL GONZALEZ HERNANDEZ ◽  
NORBERTO HERNANDEZ ROMERO ◽  
AARON RODRIGUEZ TREJO ◽  
SERGIO V. CHAPA VERGARA
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Cellular Automata ◽  
Linear Systems ◽  
Configuration Space ◽  
Integration Method ◽  
Numerical Calculations ◽  
Linear Dynamical Systems ◽  
Original Part

This paper exposes a procedure for modeling and solving linear systems using continuous-valued cellular automata. The original part of this work consists on showing how the cells in the automaton may contain both real values and operators for carrying out numerical calculations and solve a desired problem. In this sense the automaton acts as a program, where data and operators are mixed in the evolution space for obtaining the correct calculations. As an example, Euler's integration method is implemented in the configuration space in order to achieve an approximated solution for a dynamical system. Three examples showing linear behaviors are presented.

scholarly journals Indépendance algébrique de logarithmes en caractéristique P

2006 ◽  
Vol 74 (3) ◽  
pp. 461-470 ◽  
Author(s):  
Laurent Denis
Keyword(s):  
Zeta Function ◽  
Rational Function ◽  
Riemann Zeta Function ◽  
Function Field ◽  
Fundamental Period ◽  
Rational Function Field ◽  
Linearly Independent ◽  
The Riemann Zeta Function ◽  
Carlitz Module ◽  
Riemann Zeta

Let k be the rational function field over the field with q elements with characteristic p. Since the work of Carlitz we know in this situation the function ζ analog of the Riemann zeta function and the function Logφ analog of the usual logarithm. We will show two main results. Firstly, if ξ denotes the fundamental period of Carlitz module, we prove that ξ, ζ(1),…, ζ(p – 2) are algebraically independent over k. Secondly if α1,…, αn are rational elements (of degree less than q/(q − 1) to ensure convergence of the logarithm) such that Logφ α1,…, Logφ αn are linearly independent over k then they are algebraically independent over k. The point is to find suitable functions taking these values and for which Mahler's method can be used.

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