Displaying similar documents to “Analytic Solutions of second order Nonlinear Difference Equations all of whose Eigenvalues are 1”

Attracting domains for semi-attractive transformations of C.

Monique Hakim (1994)

Publicacions Matemàtiques

Similarity:

Let F be a germ of analytic transformation of (C, 0). We say that F is semi-attractive at the origin, if F' has one eigenvalue equal to 1 and if the other ones are of modulus strictly less than 1. The main result is: either there exists a curve of fixed points, or F - Id has multiplicity k and there exists a domain of attraction with k - 1 petals. We also study the case where F is a global isomorphism of C and F - Id has multiplicity k at the origin. This work has been inspired by two...

Exact asymptotics of nonlinear difference equations with levels 1 and 1 +

G.K Immink (2008)

Annales de la faculté des sciences de Toulouse Mathématiques

Similarity:

We study a class of nonlinear difference equations admitting a 1 -Gevrey formal power series solution which, in general, is not 1 - (or Borel-) summable. Using right inverses of an associated difference operator on Banach spaces of so-called , we prove that this formal solution can be lifted to an analytic solution in a suitable domain of the complex plane and show that this analytic solution is an of the formal power series.

A new proof of multisummability of formal solutions of non linear meromorphic differential equations

Jean-Pierre Ramis, Yasutaka Sibuya (1994)

Annales de l'institut Fourier

Similarity:

We give a new proof of multisummability of formal power series solutions of a non linear meromorphic differential equation. We use the recent Malgrange-Ramis definition of multisummability. The first proof of the main result is due to B. Braaksma. Our method of proof is very different: Braaksma used Écalle definition of multisummability and Laplace transform. Starting from a preliminary normal form of the differential equation x d y → d x = G → 0 ( x ) + λ ( x ) + A 0 y → + x μ G → ( x , y → ) , the idea of our proof is to interpret...

Asymptotic analysis of a class of functional equations and applications

P. J. Grabner, H. Prodinger, R. F. Tichy (1993)

Journal de théorie des nombres de Bordeaux

Similarity:

Flajolet and Richmond have invented a method to solve a large class of divide-and-conquer recursions. The essential part of it is the asymptotic analysis of a certain generating function for z → ∞ by means of the Mellin transform. In this paper this type of analysis is performed for a reasonably large class of generating functions fulfilling a functional equation with polynomial coefficients. As an application, the average life time of a party of N people is computed, where each person advances...