Complexity of Puiseux solutions of differential and $q$-difference equations of order and degree one [PDF]
arXiv, 2023 We relate the complexity of both differential and $q$-difference equations of order one and degree one and their solutions. Our point of view is to show that if the solutions are complicated, the initial equation is complicated too. In this spirit, we bound from below an invariant of the differential or $q$-difference equation, the height of its Newton
Ayuso, Pedro Fortuny +2 more
arxiv +2 more sources
On the convergence of generalized power series solutions of q-difference equations [PDF]
, 2021 A sufficient condition for the convergence of a generalized formal power series solution to an algebraic q-difference equation is provided. The main result leans on a geometric property related to the semi-group of (complex) power exponents of such a ...
Gontsov, Renat +2 more
core +1 more source
The forbidden set, solvability and stability of a circular system of complex Riccati type difference equations [PDF]
, 2023 In this paper, the circular system of Riccati type complex difference equations of the form $ u_{n+1}^{(j)} = \frac{a_ju_n^{(j-1)}+b_j}{c_ju_n^{(j-1)}+d_j}, \; n = 0, 1, 2, \cdots, \; j = 1, 2, \cdots, k, $ where $ u_n^{(0)}: = u_n^{(k)} $ for
George L. Karakostas
core +1 more source
Elementary exact calculations of degree growth and entropy for discrete equations [PDF]
, 2017 Second-order discrete equations are studied over the field of rational functions C(z)C(z), where z is a variable not appearing in the equation. The exact degree of each iterate as a function of z can be calculated easily using the standard calculations ...
Halburd, RG
core +1 more source
New class of practically solvable systems of difference equations of hyperbolic-cotangent-type [PDF]
, 2020 The systems of difference equations $$x_{n+1}=\frac{u_nv_{n-2}+a}{u_n+v_{n-2}},\quad y_{n+1}=\frac{w_ns_{n-2}+a}{w_n+s_{n-2}},\quad n\in\mathbb{N}_0,$$ where $a, u_0, w_0, v_j, s_j$ $j=-2,-1,0,$ are complex numbers, and the sequences $u_n$, $v_n,$ $w_n$,
Stevic, Stevo
core +3 more sources
Los mediadores de lectura de la comunidad y sus estilos : Estudio de casos en Biblioteca Solidaria [PDF]
, 2020 El trabajo que aquí se presenta tiene por propósito profundizar el conocimiento sobre los mediadores que leen a los niños en las escuelas públicas de Uruguay y sus estilos, que se desempeñan en el proyecto Biblioteca Solidaria de la ANEP. La mediación de
Mosca, Sandra
core +1 more source
Some applications of Nevanlinna theory to entire functions that share a small function with two difference operators [PDF]
summary:In this work, we are implementing some applications of Nevanlinna theory to entire functions that share a small function with two difference operators and we also generalize one of the results in the paper [3]
Miloudi, Boudaoud
core +1 more source
Zero entropy for some birational maps of C² [PDF]
, 2019 In this study, we consider a special case of the family of birational maps f:C² → C² , which were dynamically classified by [13]. We identify the zero entropy subfamilies of f and explicitly give the associated invariant fibrations.
Cimà, Anna, Zafar, Sundus
core +2 more sources
New solvable class of product-type systems of difference equations on the complex domain and a new method for proving the solvability [PDF]
, 2016 This paper continues the investigation of solvability of product-type systems of difference equations, by studying the following system with two variables: $$z_n=\alpha z_{n-1}^aw_{n-2}^b,\quad w_n=\beta w_{n-3}^cz_{n-2}^d,\quad n\in\mathbb{N}_0,$$ where
Stevic, Stevo
core +2 more sources
Complexity of Puiseux solutions of differential and q -difference equations of order and degree one [PDF]
We relate the complexity of both differential and q-difference equations of order one and degree one and their solutions. Our point of view is to show that if the solutions are complicated, the initial equation is complicated too.
Cano Torres, José María +2 more
core +4 more sources