On the asymptotics with respect to a parameter of solutions of differential systems with coefficients in the class L q

Vagabov, A. I.

doi:10.1134/s0012266110010039

Cited by 4 publications

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“…While this computation does not require fancy machinery, it will require some results about asymptotic formulas of solutions to the parallel transport equation corresponding to ∇ ξ . For this part, we mainly use techniques that can be found in [IV10], [Lev48] and [Was87].…”

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confidence: 99%

The Ooguri-Vafa space as a moduli space of framed wild harmonic bundles

Tulli¹

2019

Preprint

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The Ooguri-Vafa hyperkähler metric is expected to be part of the local model of the L 2 -hyperkähler metric of the Hitchin moduli spaces, near the generic part of the discriminant locus (see [Nei13]). In this paper, we show that the Ooguri-Vafa space can be interpreted as a certain set of rank 2, framed wild harmonic bundles over CP 1 , with one irregular singularity. Along the way, we also find that the electric and magnetic twistor coordinates from [GMN10], which describe the hyperkähler geometry of the Ooguri-Vafa space, have an interpretation in terms of Stokes data associated to our framed wild harmonic bundles.

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confidence: 99%

The Ooguri-Vafa space as a moduli space of framed wild harmonic bundles

Tulli¹

2019

Preprint

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Asymptotic analysis of solutions of ordinary differential equations with distribution coefficients

Савчук¹,

Шкаликов²

2020

Sb. Math.

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Ordinary differential equations of the form on the finite interval are under consideration. Here the functions and are absolutely continuous and positive and the coefficients of the differential expression are subject to the conditions where denotes the th antiderivative of the function in the sense of distributions. Our purpose is to derive analogues of the classical asymptotic Birkhoff-type representations for the fundamental system of solutions of the above equation with respect to the spectral parameter as in certain sectors of the complex plane . We reduce this equation to a system of first-order equations of the form where is a positive function, is a matrix with constant elements, the elements of the matrices and are integrable functions, and as . For systems of this kind, we obtain new results concerning the asymptotic representation of the fundamental solution matrix, which we use to make an asymptotic analysis of the above scalar equations of high order. Bibliography: 44 titles.

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On Solutions of Systems of Differential Equations on Half-Line with Summable Coefficients

Kuznetsova

2024

Lobachevskii J Math

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On the asymptotics with respect to a parameter of solutions of differential systems with coefficients in the class L q

Cited by 4 publications

References 0 publications

The Ooguri-Vafa space as a moduli space of framed wild harmonic bundles

The Ooguri-Vafa space as a moduli space of framed wild harmonic bundles

Asymptotic analysis of solutions of ordinary differential equations with distribution coefficients

On Solutions of Systems of Differential Equations on Half-Line with Summable Coefficients

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