Stokes matrices of a reducible double confluent Heun equation via monodromy matrices of a reducible general Heun equation with symmetric finite singularities
type: Item
instance of: scholarly article
title: Stokes matrices of a reducible double confluent Heun equation via monodromy matrices of a reducible general Heun equation with symmetric finite singularities
zbMATH Open document ID: 1491.34098
author: Tsvetana Stoyanova
published in: Journal of Dynamical and Control Systems
publication date: 2022-01-24T00:00:00Z
review text: In this paper, the author studies the relation between the analytic invariants of the double confluent Heun operator (DCHO) and general Heun operator (GHO). The case is considered when the linear operator \(L\in\)DCHO is reducible. That is, \(L=L_{1}\circ L_{2}\) and there are depending on a small complex parameter \(\varepsilon\) linear operators \(L_{1\varepsilon}\), \(L_{2\varepsilon}\) such that \(\lim\limits _{\varepsilon\rightarrow0}L_{\mathrm{i\varepsilon}}=L_{i}(i=1,2)\) and \(L_{\varepsilon}=L_{1\varepsilon}\circ L_{2\varepsilon}\in\) GHO. Then, as the author shows, the analytical invariants of the \(L\) can be obtained from the analytical invariants of the \(L_{\varepsilon}\) by a limit transition on \(\varepsilon\). This is particularly true for the Stokes matrices.
Mathematics Subject Classification ID: 34M35
Mathematics Subject Classification ID: 34M40
Mathematics Subject Classification ID: 34M03
Mathematics Subject Classification ID: 34A25
zbMATH DE Number: 7462072
zbMATH Keywords: reducible general Heun and double confluent Heun equations
zbMATH Keywords: unfolding
zbMATH Keywords: Stokes phenomenon
zbMATH Keywords: 1-summability
zbMATH Keywords: irregular singularity
zbMATH Keywords: monodromy matrices
zbMATH Keywords: regular singularity
zbMATH Keywords: limit
reviewed by: Mykola Grygorenko
MaRDI profile type: Publication
full work available at URL: s10883-021-09571-0
OpenAlex ID: W3197153568
cites work: Q5519244
cites work: On monodromy eigenfunctions of Heun equations and boundaries of phase-lock areas in a model of overdamped Josephson effect
cites work: On determinants of modified Bessel functions and entire solutions of double confluent Heun equations
cites work: Holomorphic solutions of the double confluent Heun equation associated with the RSJ model of the Josephson junction
cites work: A Riemann-Hilbert approach to the Heun equation
cites work: Q4254405
cites work: Solutions for confluent and double-confluent Heun equations
cites work: On the derivatives of the Heun functions
cites work: Stokes operators via limit monodromy of generic perturbation
cites work: Q3371981
cites work: Resonant confluence of singular points and Stokes phenomena
cites work: Q5797273
cites work: Heun functions and some of their applications in physics
cites work: Complete system of analytic invariants for unfolded differential linear systems with an rank \(k\) irregular singularity of Poincaré
cites work: Appell hypergeometric expansions of the solutions of the general Heun equation
cites work: Expansions of the solutions of the general Heun equation governed by two-term recurrence relations for coefficients
cites work: Confluence of singularities of nonlinear differential equations via Borel-Laplace transformations
cites work: Stokes phenomenon and confluence in non-autonomous Hamiltonian systems
cites work: Complete system of analytic invariants for unfolded differential linear systems with an irregular singularity of Poincar\'e rank 1
cites work: Q5404554
cites work: The Stokes phenomenon in the confluence of the hypergeometric equation using Riccati equation
cites work: Divergent series, summability and resurgence II. Simple and multiple summability
cites work: Q3209417
cites work: Q5310116
cites work: On the solutions of double confluent Heun equations
cites work: Antiquantization of the Double Confluent Heun Equation. The Teukolsky Equation
cites work: Divergent series, summability and resurgence I. Monodromy and resurgence
cites work: Q3997735
cites work: Q4490853
cites work: Zero level perturbation of a certain third-order linear solvable ODE with an irregular singularity at the origin of Poincaré rank 1
cites work: Solution space monodromy of a special double confluent Heun equation and its applications
cites work: Q5343650
cites work: Q5284757
DOI: 10.1007/S10883-021-09571-0
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description: scientific article; zbMATH DE number 7462072