On a reduction of nonlinear ordinary differential equations at an irregular type singularity

Po Fang Hsieh

Displaying similar documents to “On a reduction of nonlinear ordinary differential equations at an irregular type singularity”

On asymptotic integrations of $x^{2} y^{''} - P (x) y = 0$

Po Fang Hsieh (1978)

Archivum Mathematicum

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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

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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 $x \frac{d \vec{y}}{d x} = {\vec{G}}_{0} (x) + [λ (x) + A_{0}] \vec{y} + x^{μ} \vec{G} (x, \vec{y}),$ the idea of our proof is to interpret...

Analytic Solutions of second order Nonlinear Difference Equations all of whose Eigenvalues are 1

Mami Suzuki (2009)

Rendiconti del Seminario Matematico della Università di Padova

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Attracting domains for semi-attractive transformations of C.

Monique Hakim (1994)

Publicacions Matemàtiques

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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...

Pseudoconcave Lie groups

Aldo Andreotti, Alan Huckleberry (1972)

Compositio Mathematica

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Real analytic manifolds in $ℂ^{n}$ with parabolic complex tangents along a submanifold of codimension one

Patrick Ahern, Xianghong Gong (2009)

Annales de la faculté des sciences de Toulouse Mathématiques

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We will classify $n$ -dimensional real submanifolds in $ℂ^{n}$ which have a set of parabolic complex tangents of real dimension $n - 1$ . All such submanifolds are equivalent under formal biholomorphisms. We will show that the equivalence classes under convergent local biholomorphisms form a moduli space of infinite dimension. We will also show that there exists an $n$ -dimensional submanifold $M$ in $ℂ^{n}$ such that its images under biholomorphisms $(z_{1}, \dots, z_{n}) \mapsto (r z_{1}, \dots, r z_{n - 1}, r^{2} z_{n})$ , $r > 1$ , are not equivalent to $M$ via any local volume-preserving...

Displaying similar documents to “On a reduction of nonlinear ordinary differential equations at an irregular type singularity”

On asymptotic integrations of x 2 y ' ' - P ( x ) y = 0

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

Analytic Solutions of second order Nonlinear Difference Equations all of whose Eigenvalues are 1

Attracting domains for semi-attractive transformations of C.

Pseudoconcave Lie groups

Real analytic manifolds in ℂ n with parabolic complex tangents along a submanifold of codimension one

On asymptotic integrations of $x^{2} y^{''} - P (x) y = 0$

Real analytic manifolds in $ℂ^{n}$ with parabolic complex tangents along a submanifold of codimension one