Confluence of singularities of nonlinear differential equations via Borel-Laplace transformations

DOI10.1007/s10883-015-9290-7zbMath1339.34095arXiv1307.8383OpenAlexW3098115157MaRDI QIDQ273808

Martin Klimeš

Publication date: 22 April 2016

Published in: Journal of Dynamical and Control Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.8383

zbMATH Keywords

ordinary differential equationsBorel summationconfluenceunfoldingirregular singularityBorel-Laplace transformationcenter manifold of a saddle-node singularity

Mathematics Subject Classification ID

Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35) Formal solutions and transform techniques for ordinary differential equations in the complex domain (34M25) Stokes phenomena and connection problems (linear and nonlinear) for ordinary differential equations in the complex domain (34M40)

Related Items (5)

Stokes phenomenon and confluence in non-autonomous Hamiltonian systems ⋮ Zero level perturbation of a certain third-order linear solvable ODE with an irregular singularity at the origin of Poincaré rank 1 ⋮ Isomonodromic Laplace transform with coalescing eigenvalues and confluence of Fuchsian singularities ⋮ Stokes matrices of a reducible double confluent Heun equation via monodromy matrices of a reducible general Heun equation with symmetric finite singularities ⋮ Coalescing Complex Planar Stationary Points

Cites Work

• Composite asymptotic expansions
• Problèmes de modules pour des équations différentielles non linéaires du premier ordre
• Summability of power series in several variables, with applications to singular perturbation problems and partial differential equations
• Monomial summability and doubly singular differential equations
• Resonant confluence of singular points and Stokes phenomena
• Summability of divergent series
• Formal power series and linear systems of meromorphic ordinary differential equations
• On the confluence phenomenon for Fuchsian equations
• On Borel summation and Stokes phenomena for rank-\(1\) nonlinear systems of ordinary differential equations
• Sur l'étude analytique des solutions d'un système d'équations différentielles dans le voisinage d'un point singulier d'indetermination. 1
• Classification of complex polynomial vector fields in one complex variable
• Complete system of analytic invariants for unfolded differential linear systems with an irregular singularity of Poincar\'e rank 1
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