Dynamical Classification of a Family of Birational Maps of C^2 via Algebraic Entropy [PDF]
arXiv, 2017 This work dynamically classifies a 9-parametric family of birational maps f : C2 -> C2. From the sequence of the degrees dn of the iterates of f, we find the dynamical degree delta(f) of f. We identify when dn grows periodically, linearly, quadratically or exponentially.
arxiv
Determination of accessory parameters in a system of the Okubo normal form [PDF]
arXiv, 2020 A system of differential equations of the Okubo normal form containing accessory parameters is considered. A condition for determining special values of the accessory parameters is given. It is shown that the special values give the differential equation satisfied by a product of the Gauss hypergeometric functions.
arxiv
Hyers-Ulam stability of parabolic Möbius difference equation [PDF]
arXiv, 2017 The linear fractional map $ g(z) = \frac{az+ b}{cz + d} $ on the Riemann sphere with complex coefficients $ ad-bc = 1 $ is and $ a+d = \pm 2 $, then $ g $ is called {\em parabolic} M\"obius map. Let $ \{ b_n \}_{n \in \mathbb{N}_0} $ be the solution of the parabolic M\"obius difference equation $ b_{n+1} = g(b_n) $ for every $ n \in \mathbb{N}_0 $.
arxiv
Espacios públicos, encuentros sociales y ritual funerario en San José de Moro : análisis de la ocupación Mochica Tardío en el Área 45, Sector Oeste de San José de Moro [PDF]
, 2011 A través de esta investigación intentamos entender un conjunto de evidencias recuperadas a partir de la excavación en el sitio arqueológico San José de Moro, ubicado en la margen derecha del río Jequetepeque, en el departamento La Libertad.
Muro Ynoñán, Luis Armando
core
Hyers-Ulam stability of loxodromic Möbius difference equation [PDF]
arXiv, 2018 Hyers-Ulam of the sequence $ \{z_n\}_{n \in \mathbb{N}} $ satisfying the difference equation $ z_{i+1} = g(z_i) $ where $ g(z) = \frac{az + b}{cz + d} $ with complex numbers $ a $, $ b $, $ c $ and $ d $ is defined. Let $ g $ be loxodromic M\"obius map, that is, $ g $ satisfies that $ ad-bc =1 $ and $a + d \in \mathbb{C} \setminus [-2,2] $.
arxiv
$Δy = e^{sy}$ or: How I Learned to Stop Worrying and Love the $Γ$-function [PDF]
arXiv, 2019 For a nice holomorphic function $f(s, z)$ in two variables, a respective holomorphic Gamma function $\Gamma = \Gamma_f$ is constructed, such that $f(s, \Gamma(s)) = \Gamma(s + 1)$. Along the way, we fall through a rabbit hole of infinite compositions, First Order Difference Equations, and absurd functional equations... This paper is orchestrated around
arxiv
Difference equations in the complex plane: quasiclassical asymptotics and Berry phase [PDF]
arXiv, 2019 We study solutions to the difference equation $\Psi(z+h)=M(z)\Psi(z)$ where $z$ is a complex variable, $h>0$ is a parameter, and $M:\mathbb{C}\mapsto SL(2,\mathbb{C})$ is a given analytic function. We describe the asymptotics of its analytic solutions as $h\to 0$.
arxiv
Quantum $K$-theory of projective spaces and confluence of $q$-difference equations [PDF]
arXiv, 2019 Givental's $K$-theoretical $J$-function can be used to reconstruct genus zero $K$-theoretical Gromov--Witten invariants. We view this function as a fundamental solution of a $q$-difference system. In the case of projective spaces, we show that we can use the confluence of $q$-difference systems to obtain the cohomological $J$-function from its $K ...
arxiv
Discrete Painlevé Equations [PDF]
arXiv, 2019 This expository article written for the Notices of the American Mathematical Society provides an overview of transcendental functions arising as solutions of the discrete Painlev\'e equations, for which the developments of the last two decades have been rich and dynamic.
arxiv
Zeros, growth and Taylor coefficients of entire solutions of linear $q$-difference equations [PDF]
Ann. Fenn. Math. 46 (2021), 249-277, 2019 We consider transcendental entire solutions of linear $q$-difference equations with polynomial coefficients and determine the asymptotic behavior of their Taylor coefficients. We use this to show that under a suitable hypothesis on the associated Newton-Puiseux diagram their zeros are asymptotic to finitely many geometric progressions.
arxiv