Titlebook: Algebraic Analysis of Differential Equations; from Microlocal Anal Takashi Aoki,Hideyuki Majima,Nobuyuki Tose Book 2008 Springer-Verlag Tok

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Some dynamical aspects of Painlevé VIWe survey some results from our recent studies on the sixth Painlevé equation as a dynamical system. We discuss such topics as phase space and its compactification, Riemann-Hilbert correspondence, Poincaré section, bounded orbits, topological entropy and dynamical degree, and periodic solutions.

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Automated Debugging for Logic Bugsts importance in the analysis of the Noumi-Yamada system (a particular higher order Painlevé equation) and a concrete recipe for locating them. Examples given here make it manifest that virtual turning points are indispensable in WKB analysis of higher order linear ordinary differential equations with a large parameter.

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https://doi.org/10.1007/978-3-319-06242-6ge time dependently. For the one space dimensional case, we developed an analogue of the probe method known for inverse boundary value problems for elliptic equations and gave a reconstruction scheme for identifying the inclusion from the Neumann to Dirichlet map.

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https://doi.org/10.1007/978-3-319-06242-6n this article we give a brief survey of the subject and known results. We then report a recently found ‘algebraic’ formula for general correlation functions. This is a joint work with Herman Boos, Tetsuji Miwa, Fedor Smirnov and Yoshihiro Takeyama.

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Debugging at the Electronic System Levelto state an inverse image theorem for .-functions of holonomic .-modules. We apply this result to an explicit calculation of the usual .-function of the Kashiwara-Hotta module on the Grothendieck’s simultaneous resolution of a semi-simple Lie algebra.

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