5 in this paper; our particular interest is in the relation between the Stokes geometry of a higher order Painlevé equation in the hierarchy and that of its underlying Lax pair. Takano, Defining manifolds for Painlevé equations, in Toward the Exact WKB Analysis of Differential Equations, Linear and Nonlinear, eds. CALL NUMBER: QC 20. ated with dynamical tunneling by following the program developed in the exact WKB analy-sis. Christopher J Howls,. Exact WKB analysis of linear differential equations: Takahiro Kawai and Yoshitsugu Takei, Introduction-Exact WKB analysis of linear differential equations; its background and prospect (3-7); Takashi Aoki, Takahiro Kawai and Yoshitsugu Takei, On a complete description of the Stokes geometry for higher order ordinary differential equations with a large parameter via integral.
Takei Kyoto University Press,, Joint editor Conference Activities & Talks On the instanton-type expansions for Painlevé transcendents and elliptic functions Yoshitsugu Takei Mar. WKB solutions are known to be J.Howls Borel summable in each Stokes region when Qj 0(j= 1;2) and Q0 is a rational function and the relation between the Borel sums in adjacent Stokes regions (i. Rasoamanana 06 J. Kyoto University Press,. Howls, Takahiro Kawai, Yoshitsugu Takei. Rasoamanana: ´ Etude r´ esurgente d’une classe d’´ equations diff´ erentielles de type Schr¨odinger. , connection formula) are also obtained. A similar analysis for the spherical partition function of N= 2 superconformal gauge theory and N= 2 gauge theory was performed in 28.
5 is essentially the same as that of Theorems 1. ) This is a joint work with T. of Washington) Boundary rigidity and the Dirichlet-to-Neumann map 13:30 – 14:30 Andr´e Voros (CEA Saclay) From exact-WKB towards singular quantum perturbation theory 15:00 – 16:00 Fr´ed´eric Pham (Univ.
Takai, Toward the Exact WKB Analysis of Differential Equations, Linear or Nonlinear, Kyoto University Press,. Toward the exact WKB analysis of differential equations, linear or non-linear. Howls 133 Some dynamical aspects of Painleve VI Toward the Exact WKB Analysis - J.Howls Katsunori Iwasaki 143 An algebraic representation for correlation functions in. Toward the Exact WKB Analysis of Differential Equations, Linear or Non-Linear C. Exact WKB analysis via computers (Joint work with N. ), Towards the Exact WKB Analysis of Differential Equations, Linear or Nonlinear.
A set of rules is given for dealing with WKB expansions in the one-dimensional analytic case, whereby such expansions are not considered as approximations but as exact encodings of wave functions, thus allowing for analytic continuation with respect to whichever parameters the potential function depends on, with an exact control of small exponential effects. Takei: An explicit description of the connection formula for the first Painleve&39; equation, " Toward the Exact WKB Analysis of Differential Equations, Linear or Non-Linear (ed. 7 of 6, we scribe its core part below in view of its importance in the main theme of this paperâ€”microlocal proach to the exact WKB analysis, WKB analysis based on the Borel transformation. Elementary and somewhat geometric proof of Painlevé property for every Painlevé equation exept for the 1st one is given. Toward the Exact WKB Analysis of Differential Equations, Linear or Non-Linear. We apply the exact.
functions of large order, in Toward the exact WKB analysis of di erential equations, linear or non-linear (Kyoto, 1998), Kyoto Univ. In this sense Stokes curves play a crucially important role in this analysis. Our focus remains the v ≫ 1 regime for the potentials V (q) = q N + vq M on the real line, with N> M positive even integers. Takei (Kyoto Univ. July 7 (Thu) -- July 14 (Thu), Lecture Hall (Room No. In Toward the Exact WKB Analysis of Differential Equations, Linear or Non-Linear, December 1998 (pp.
Koike) 11:00 – 12:00 Gunther Uhlmann (Univ. Koike, On a regular singular point in the exact WKB analysis, "Toward the Exact WKB Analysis of Differential Equations, Linear or Non-linear (Kyoto, 1998)", Kyoto Univ. W53 T6 CIMM : AUTHOR: Kimmel, Marek, 1959- TITLE: Branching processes in biology / Marek Kimmel, David E. Toward the exact WKB analysis of differential equations linear or non-linear (C. Kyoto, Japan : Kyoto University Press, © (OCoLC: Named Person: Gregor Wentzel; Hendrik Anthony Kramers; Léon Brillouin: Document Type: Book: All Authors / Contributors: Christopher J Howls; Takahiro Kawai; Yoshitsugu Takei.
Defining Manifolds for Painlevé Equations, "Toward the exact WKB analysis of differential equations, linear or non-linear" (Eds. Press,, 39--53. 複素微分方程式 (ふくそびぶんほうていしき、英: Complex differential equations) とは複素関数を厳密解としてもつ微分方程式の総称であり、その解析には解析接続やモノドロミー行列をはじめとした複素解析の道具が用いられる. Geometric properties of the Riemann surfaces associated with the Noumi-Yamada systems with a large parameter. Exact WKB Toward the Exact WKB Analysis - J.Howls analysis near a simple turning point Eric Delabaere 101 The Borel transform Leon Ehrenpreis 119 On the use of Z-transforms in the summation of transseries for partial differential equations Christopher J. Toward the Exact WKB Analysis of the P II Hierarchy Yukihiro Nishikawa Hitachi Ltd. At the Ramis Conference held at Toulouse in September in, as a gen-. Contents: Part I.
, Asagayakitaguchichiekimae‐Building 2‐13‐2, Asagayakita, Suginami‐ku, Tokyo, 166‐0001, Japan. Algebraic Analysis of Differential Equations--- from Microlocal Analysis to Exponential Asymptotics ---in honor of Prof. We believe that our attempt provides a good testing ground of the exact WKB framework as well, as it leads to checking the applicability of newly proposed notions such as virtual turn-ing points and new Stokes curves 19–21. This note continues our study 1 of singular perturbation theory in onedimensional (1D) quantum mechanics using exact WKB analysis.
One of our motivations is to generalize Theorem 1. : Microdifferential Systems in the Complex Domain, Grundlehren Der Mathematischen Wissenschaften, Springer-Verlag (1985) T Takei, Y. Exact WKB analysis of 2nd-order non-homogeneous equations 295 passing through x0 can be prolonged to x= 1 without ﬂowing into any turning point, then the WKB solutions ±(x; ) normalized at x0 are Borel summable in a neighborhood of x0. , English, Public lecture, seminar, tutorial, course. Takei, “On a complete description of the Stokes geometry for higher order ordinary differential equations with a large parameter via integral representations,” Toward the Exact WKB Analysis of Differential Equations, Linear or Non-Linear (Kyoto University Press, Kyoto, ), pp. Toward the Exact WKB Analysis of Differential Equations, Linear or Non-Linear, Kyoto, Japan. Takahiro KAWAI on the occasion of his sixtieth birthday.
Koike, and partly with N. Toward the exact WKB analysis for instanton-type solutions of Painlev e hierarchies Yoshitsugu Takei (RIMS, Kyoto Univ. 420) of RIMS (for July 7, 8), International Conference Hall of the Clock Tower (for July 11--14), Kyoto. Howls, Hyperasymptotics for multidimensional Laplace integrals with boundaries&39;&39; in Toward the Exact WKB Analysis of Differential Equations, Linear or Non-Linear (Kyoto, 1998), Kyoto Univ. Kyoto University Press () pp. ), Kyoto University Press (),71-85. Although the oof of Theorems 3. From exact-WKB toward singular quantum perturbation.
TakeiOn the exact WKB analysis for higher order ordinary differential equations with a large parameter Asian J. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): the exact WKB analysis for instanton-type solutions of Painleve hierarchies. de Nice-Sophia Antipolis). Koike, On the perturbation series in large order of anharmonic oscillators, Annales Henri Poincare,,. , second order) Painleve equations, we have now been trying to develop a program to analyze (PJ) (J = I, II or IV) hierarchies of higher order Painleve equations. , Delabaere-Dillinger-Pham 93) follow from periodicity of corresponding. Exact WKB analysis near a simple turning point. Japan; Volume 63, Number,.
Toward the exact WKB analysis of differential equations, linear or non-linear / edited by Christopher J. PUBLISHER: Kyoto : Kyoto University Press, c. CrossRef View Record in Scopus Google Scholar. Microlocal analysis and exponential asymptotics are intimately connected and provide powerful tools that have been applied to linear and non-linear differential equations as well as many related fields such as real and complex analysis, integral transforms, spectral theory, inverse problems, integrable systems, and mathematical physics. Takei), 261-269, Kyoto Univ. The exact WKB analysis, which has been developed mainly in mathematics since the pioneering work by Voros in 1983, is a powerful tool to an- alyze Stokes phenomena of Schrodinger-type dierential equations. We develop the exact WKB analysis of the P II hierarchy introduced by Gordoa et al.
•Main result: We add Exact WKB analysis in the above list: skew-symmetric matrix B ↔ Stokes graph cluster variables ↔ Voros symbols cluster mutation ↔ Stokes phenomenon (for →∞) •Application: Identities of Stokes automorphsims in the exact WKB analysis (c. The paper 29 studies the Mathieu equation in the context of exact WKB and the 2d/4d correspondence, as we shall do. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): generalization of the exact WKB analysis for traditional (i. However, in our case Q0(z) = 1 (1+z2)2 1. Primary Publications : T. 1 to non-homogeneous equations. Toward the Exact WKB Analysis - J.Howls : Toward the exact WKB analysis for higher-order Painlev´.
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