scholarly journals Linear difference equations, frieze patterns, and the combinatorial Gale transform

2014 ◽  
Vol 2 ◽  
Author(s):  
SOPHIE MORIER-GENOUD ◽  
VALENTIN OVSIENKO ◽  
RICHARD EVAN SCHWARTZ ◽  
SERGE TABACHNIKOV
Keyword(s):  
Projective Space ◽  
Periodic Solutions ◽  
Difference Equations ◽  
Moduli Space ◽  
Gauss Map ◽  
Rational Maps ◽  
Linear Difference Equations ◽  
Periodic Coefficients ◽  
Gale Transform

AbstractWe study the space of linear difference equations with periodic coefficients and (anti)periodic solutions. We show that this space is isomorphic to the space of tame frieze patterns and closely related to the moduli space of configurations of points in the projective space. We define the notion of a combinatorial Gale transform, which is a duality between periodic difference equations of different orders. We describe periodic rational maps generalizing the classical Gauss map.

Oscillations in a class of linear difference equations with periodic coefficients

1994 ◽  
Vol 53 (3-4) ◽  
pp. 175-183 ◽  
Author(s):  
CH. G. Philos ◽  
I. K. Purnaras
Keyword(s):  
Difference Equations ◽  
Linear Difference Equations ◽  
Periodic Coefficients

scholarly journals On the geometry of bifurcation currents for quadratic rational maps

2014 ◽  
Vol 35 (5) ◽  
pp. 1369-1379 ◽  
Author(s):  
FRANÇOIS BERTELOOT ◽  
THOMAS GAUTHIER
Keyword(s):  
Projective Space ◽  
Moduli Space ◽  
Complex Projective Space ◽  
The Self ◽  
Rational Maps ◽  
Two Dimensional ◽  
Lelong Numbers ◽  
Complex Projective

We describe the behaviour at infinity of the bifurcation current in the moduli space of quadratic rational maps. To this purpose, we extend it to some closed, positive $(1,1)$-current on a two-dimensional complex projective space and then compute the Lelong numbers and the self-intersection of the extended current.

scholarly journals ON A SOLVABLE SYSTEM OF NON-LINEAR DIFFERENCE EQUATIONS WITH VARIABLE COEFFICIENTS

2021 ◽  
Vol 21 (1) ◽  
pp. 145-162
Author(s):  
MERVE KARA ◽  
YASIN YAZLIK
Keyword(s):  
Closed Form ◽  
Periodic Solutions ◽  
Difference Equations ◽  
Variable Coefficients ◽  
Linear Difference Equations ◽  
System Of Difference Equations ◽  
Solvable System ◽  
Initial Values ◽  
Non Linear ◽  
Forbidden Set

In this paper, we show that the system of difference equations can be solved in the closed form. Also, we determine the forbidden set of the initial values by using the obtained formulas. Finally, we obtain periodic solutions of aforementioned system.

scholarly journals On the oscillation of some linear difference equations with periodic coefficients

1997 ◽  
Vol 84 (2) ◽  
pp. 219-241 ◽  
Author(s):  
I.-G.E. Kordonis ◽  
Ch.G. Philos ◽  
I.K. Purnaras
Keyword(s):  
Difference Equations ◽  
Linear Difference Equations ◽  
Periodic Coefficients

scholarly journals Sensitivity of Schur stability of systems of linear difference equations with periodic coefficients

2016 ◽  
Vol 4 (2) ◽  
pp. 159-159
Author(s):  
Ahmet Duman ◽  
Gulnur Celik Kizilkan ◽  
Kemal Aydin
Keyword(s):  
Difference Equations ◽  
Linear Difference Equations ◽  
Periodic Coefficients ◽  
Schur Stability

scholarly journals Exact solution of a difference approximation to Duffing's equation

1981 ◽  
Vol 23 (1) ◽  
pp. 64-77 ◽  
Author(s):  
Renfrey B. Potts
Keyword(s):  
Exact Solution ◽  
Closed Form ◽  
Periodic Solutions ◽  
Difference Equations ◽  
Difference Approximation ◽  
Linear Difference Equations ◽  
Duffing's Equation ◽  
Duffing’S Equation ◽  
Non Linear

AbstractDuffing's equation, in its simplest form, can be approximated by various non-linear difference equations. It is shown that a particular choice can be solved in closed form giving periodic solutions.

scholarly journals Eventually Periodic Solutions for Difference Equations with Periodic Coefficients and Nonlinear Control Functions

2008 ◽  
Vol 2008 ◽  
pp. 1-21 ◽  
Author(s):  
Chengmin Hou ◽  
Sui Sun Cheng
Keyword(s):  
Nonlinear Control ◽  
Periodic Solutions ◽  
Difference Equations ◽  
Nonlinear Filtering ◽  
Nonlinear Difference Equations ◽  
Periodic Coefficients ◽  
Periodic Sequences ◽  
Control Functions ◽  
Filtering Function

For nonlinear difference equations of the formxn=F(n,xn−1,…,xn−m), it is usually difficult to find periodic solutions. In this paper, we consider a class of difference equations of the formxn=anxn−1+bnf(xn−k), where{an},  {bn}are periodic sequences andfis a nonlinear filtering function, and show how periodic solutions can be constructed. Several examples are also included to illustrate our results.

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