scholarly journals Existence of homoclinic orbits for a higher order difference system

2017 ◽  
Vol 10 (04) ◽  
pp. 1842-1853 ◽  
Author(s):  
Xia Liu ◽  
Tao Zhou ◽  
Haiping Shi
Keyword(s):  
Homoclinic Orbits ◽  
Higher Order ◽  
Difference System ◽  
Order Difference

scholarly journals An infinite family of higher-order difference operators that commute with Ruijsenaars operators of type A

2021 ◽  
Vol 111 (4) ◽  
Author(s):  
Masatoshi Noumi ◽  
Ayako Sano
Keyword(s):  
Infinite Family ◽  
Type A ◽  
Higher Order ◽  
Difference Operators ◽  
Order Difference

AbstractWe introduce a new infinite family of higher-order difference operators that commute with the elliptic Ruijsenaars difference operators of type A. These operators are related to Ruijsenaars’ operators through a formula of Wronski type.

scholarly journals Symmetries and Solvability of a Class of Higher Order Systems of Ordinary Difference Equations

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 108
Author(s):  
Kgatliso Mkhwanazi ◽  
Mensah Folly-Gbetoula
Keyword(s):  
Difference Equations ◽  
Variable Coefficients ◽  
Higher Order ◽  
Order Difference

We perform Lie analysis for a system of higher order difference equations with variable coefficients and derive non-trivial symmetries. We use these symmetries to find exact formulas for the solutions in terms of k. Furthermore, a detailed study for a specific value of k is presented. Our findings generalize some results in the literature.

scholarly journals Fixed Points of Meromorphic Functions and Their Higher Order Differences and Shifts

2019 ◽  
Vol 17 (1) ◽  
pp. 677-688 ◽  
Author(s):  
Hai-Ying Chen ◽  
Xiu-Min Zheng
Keyword(s):  
Fixed Points ◽  
Meromorphic Functions ◽  
Higher Order ◽  
Order Difference ◽  
First Order ◽  
Special Points ◽  
And Shifts

Abstract In this paper, we investigate the relationships between fixed points of meromorphic functions, and their higher order differences and shifts, and generalize the case of fixed points into the more general case for first order difference and shift. Concretely, some estimates on the order and the exponents of convergence of special points of meromorphic functions and their differences and shifts are obtained.

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