WKB Analysis and Stokes Geometry of Differential Equations

DOI10.1007/978-3-319-52842-7_5zbMath1404.34110OpenAlexW2630423661MaRDI QIDQ4644995

Yoshitsugu Takei

Publication date: 9 January 2019

Published in: Trends in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-52842-7_5

zbMATH Keywords

monodromy groupcompletely integrable systemwall crossing formulaexact WKB analysisnew Stokes curvevirtual turning pointWKB solutionStokes geometryBorel resummationconnection formula

Mathematics Subject Classification ID

Singular perturbations, turning point theory, WKB methods for ordinary differential equations (34E20) Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35) Asymptotics and summation methods for ordinary differential equations in the complex domain (34M30) Stokes phenomena and connection problems (linear and nonlinear) for ordinary differential equations in the complex domain (34M40) Singular perturbation problems for ordinary differential equations in the complex domain (complex WKB, turning points, steepest descent) (34M60)

Related Items (15)

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Cites Work

• Spectral networks
• Voros resurrection and periods of hyperelliptic curves
• From divergent power series to analytic functions. Theory and application of multisummable power series
• On the exact WKB analysis of operators admitting infinitely many phases.
• On the exact WKB analysis of microdifferential operators of WKB type.
• Wall-crossing, Hitchin systems, and the WKB approximation
• Spectral networks and snakes
• On a WKB-theoretic transformation for a completely integrable system near a degenerate point where two turning points coalesce
• New Stokes’ line in WKB theory
• Exact semiclassical expansions for one-dimensional quantum oscillators
• Virtual turning points and bifurcation of Stokes curves for higher order ordinary differential equations
• Virtual Turning Points
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