2017 academic year

No. 1

Date: April 25 (Tue) 16:30 - 17:30

Place: B707, Fac. Sci., Hiroshima University

Speaker: Toshinori TAKAHASHI (Osaka University of Health and Sport sciences)

Title:The confluent hypergeometric function and WKB solutions

Abstract:

    The confluent hypergeometric function is one of the solutions of the confluent hypergeometric differential equation. In this talk, we analyze the equation by using the exact WKB analysis and give an explicit formula which describes the relation between the confluent hypergeometric function and WKB solutions.

No. 2

Date: July 5 (Wed) 15:30 - 17:30

Place: B707, Fac. Sci., Hiroshima University

Speaker:Shogo YAMANAKA (Kyoto University)

Title:Normal forms of general dynamical systems and their integrability

Abstract:

    Normal forms near equilibria, which are called Poincar\'e-Dulac normal forms for general systems and Birkhoff normal forms for Hamiltonian systems, have extensively studied. In particular, it is well known that integrable systems are analytically transformed to normal forms for the two cases. However, normal forms may be nonintegrable. In this talk, we discuss conditions that Poincar\'e-Dulac normal forms are integrable, after reviewing the theory of Birkhoff normal forms and their integrability. We also discribe a relation between integrability of Poincar\'e-Dulac normal forms and their resonance degrees.

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