2021/01/08 by Jun Xia, Xia, Jun, Shuai‐Xia Xu +3
Mathematics · Physics and Astronomy · #33E17 #34A30 #34E05 #34M55 #41A60 #Algebraic structures and combinatorial models #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics
paper · pdf · doi:10.48550/arxiv.2101.02864
openalex publication_date 2021/01/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we consider the monodromy and, in particularly, the isomonodromy sets of accessory parameters for the Heun class equations. We show that the Heun class equations can be obtained as limits of the linear systems associated with the Painlevé equations when the Painlevé transcendents go to one of the actual singular points of the linear systems. While the isomonodromy sets of accessory parameters for the Heun class equations are described by the Taylor or Laurent coefficients of the corresponding Painlevé functions, or the associated tau functions, at the positions of the critical values. As an application of these results, we derive some asymptotic approximations for the isomonodromy sets of accessory parameters in the Heun class equations, including the confluent Heun equation, the doubly-confluent Heun equation and the reduced biconfluent Heun equation.