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| 担当者 | 大島 利雄, 坂井 秀隆 |
|---|
2016年12月06日(火)
16:45-18:15 数理科学研究科棟(駒場) 154号室
David Sauzin 氏 (CNRS)
Introduction to resurgence on the example of saddle-node singularities (ENGLISH)
David Sauzin 氏 (CNRS)
Introduction to resurgence on the example of saddle-node singularities (ENGLISH)
[ 講演概要 ]
Divergent power series naturally appear when solving such an elementary differential equation as x^2 dy = (x+y) dx, which is the simplest example of saddle-node singularity. I will discuss the formal classification of saddle-node singularities and illustrate on that case Ecalle's resurgence theory, which allows one to analyse the divergence of the formal solutions. One can also deal with resonant saddle-node singularities with one more dimension, a situation which covers the local study at infinity of some Painlevé equations.
Divergent power series naturally appear when solving such an elementary differential equation as x^2 dy = (x+y) dx, which is the simplest example of saddle-node singularity. I will discuss the formal classification of saddle-node singularities and illustrate on that case Ecalle's resurgence theory, which allows one to analyse the divergence of the formal solutions. One can also deal with resonant saddle-node singularities with one more dimension, a situation which covers the local study at infinity of some Painlevé equations.
