×

Solution with movable singular points of some Hamiltonian system. (English) Zbl 1515.37063

Filipuk, Galina (ed.) et al., Recent trends in formal and analytic solutions of diff. equations. Virtual conference, University of Alcalá, Alcalá de Henares, Spain, June 28 – July 2, 2021. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 782, 207-218 (2023).
Summary: This paper studies the movable singular points of a solution of the Hamiltonian system with the Hamiltonian \(H:=H_0+H_1\). Here \(H_0\) is integrable and the Hamiltonian system of \(H_0\) has a singular solution \(v\), while \(H_1\) is a perturbation. A singular solution for \(H\) is given as \(F(v)\) for some transformation \(F\) being defined in the domain of the phase space which contains the orbit of \(v\) tending to the infinity. The map \(F\) is given by the homology equation via the global Borel summability.
For the entire collection see [Zbl 1508.30067].

MSC:

37J65 Nonautonomous Hamiltonian dynamical systems (Painlevé equations, etc.)
34M25 Formal solutions and transform techniques for ordinary differential equations in the complex domain
34M30 Asymptotics and summation methods for ordinary differential equations in the complex domain
34M35 Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms
40C15 Function-theoretic methods (including power series methods and semicontinuous methods) for summability
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Filipuk, G., Movable algebraic singularities of second-order ordinary differential equations, J. Math. Phys., 023509, 18 pp. (2009) · Zbl 1202.34152 · doi:10.1063/1.3068414
[2] Kawai, Takahiro, Algebraic analysis of singular perturbation theory, Translations of Mathematical Monographs, xiv+129 pp. (2005), American Mathematical Society, Providence, RI · Zbl 1100.34004 · doi:10.1090/mmono/227
[3] Yoshino, Masafumi, Movable singularity of semi linear Heun equation and application to blowup phenomenon, NoDEA Nonlinear Differential Equations Appl., Paper No. 8, 18 pp. (2019) · Zbl 1409.35011 · doi:10.1007/s00030-019-0555-9
[4] Masafumi Yoshino, Global Borel summability of some partial differential equation, To be published in the Proceedings of “Formal and Analytic Solutions of Differential Equations”, World Scientific Publishing Europe Ltd. DOI: 10.1142/q0335, ISBN: 978-1-80061-135-1.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.