Monomial summability and doubly singular differential equations
Copyright policy )Monomial summability and doubly singular differential equations
In this work, we consider systems of differential equations that are doubly singular, i.e. that are both singularly perturbed and exhibit an irregular singular point. Under a condition that also guanrantees the existence of a unique formal solution, we show that this formal solution is monomially summable, i.e. summable with respect to the monomial in the independent variable and in the parameter in a (new) sense that will be defined. As a preparation, Poincaré asymptotics and Gevrey asymptotics in a monomial are studied.
Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms, ordinary differential equations, summability, [MATH.MATH-CV] Mathematics [math]/Complex Variables [math.CV], irregular singular points, Dynamical aspects of holomorphic foliations and vector fields, Singular perturbation problems for ordinary differential equations in the complex domain (complex WKB, turning points, steepest descent), asymptotic expansions, singular perturbation, [MATH.MATH-CA] Mathematics [math]/Classical Analysis and ODEs [math.CA], Analysis
Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms, ordinary differential equations, summability, [MATH.MATH-CV] Mathematics [math]/Complex Variables [math.CV], irregular singular points, Dynamical aspects of holomorphic foliations and vector fields, Singular perturbation problems for ordinary differential equations in the complex domain (complex WKB, turning points, steepest descent), asymptotic expansions, singular perturbation, [MATH.MATH-CA] Mathematics [math]/Classical Analysis and ODEs [math.CA], Analysis
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