A new proof of summability of formal solutions of nonlinear meromorphic differential equations

DOI10.5802/aif.1418zbMath0812.34005OpenAlexW2330233662MaRDI QIDQ1341638

Yasutaka Sibuya, Jean Pierre Ramis

Publication date: 8 January 1995

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_1994__44_3_811_0

zbMATH Keywords

normal formsresonancesexponential decaynonlinear Stokes phenomenonmultisummabilityformal power series solutionsnonlinear meromorphic differential equations

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Functional analytic methods in summability (40H05) Ordinary differential equations in the complex domain (34M99) Abel, Borel and power series methods (40G10)

Related Items (22)

On the summability of a class of formal power series ⋮ On parametric multisummable formal solutions to some nonlinear initial value Cauchy problems ⋮ Multisummability of formal power series solutions of partial differential equations with constant coefficients ⋮ On the convergence of generalized power series satisfying an algebraic ODE ⋮ On singularly perturbed linear initial value problems with mixed irregular and Fuchsian time singularities ⋮ On functions uniquely determined by their asymptotic expansion ⋮ Multisummability in Carleman ultraholomorphic classes by means of nonzero proximate orders ⋮ The Gevrey asymptotics in the initial value problem for singularly perturbed nonlinear differential equations ⋮ Stable manifolds of biholomorphisms in Cn$\mathbb {C}^n$ asymptotic to formal curves ⋮ Trajectories in interlaced integral pencils of 3-dimensional analytic vector fields are o-minimal ⋮ Recent progress in the theory of formal solutions for ODE and PDE. ⋮ On the summability of formal solutions for doubly singular nonlinear partial differential equations ⋮ Unnamed Item ⋮ On parametric Gevrey asymptotics for some Cauchy problems in quasiperiodic function spaces ⋮ Asymptotic Analysis and Summability of Formal Power Series ⋮ Accelero-summation of the formal solutions of nonlinear difference equations ⋮ Stokes coefficients of the cubic model: a quantum resurgence viewpoint ⋮ On singularly perturbed small step size difference-differential nonlinear PDEs ⋮ On a conjecture of Fefferman and Graham ⋮ Equivalence of three-dimensional Cauchy-Riemann manifolds and multisummability theory ⋮ Summability in general Carleman ultraholomorphic classes ⋮ Strongly regular sequences and proximate orders

Cites Work

• Intégration analytique d'un système d'équations différentielles non linéaires dans le voisinage d'un point singulier. I, II
• Multisummability and Stokes multipliers of linear meromorphic differential equations
• Multisummable functions
• Multisummability of formal power series solutions of nonlinear meromorphic differential equations
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