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Classical Analysis
Seminar information archive ～10/09｜Next seminar｜Future seminars 10/10～
2016/12/06
16:45-18:15 Room #154 (Graduate School of Math. Sci. Bldg.)
David Sauzin (CNRS)
Introduction to resurgence on the example of saddle-node singularities (ENGLISH)
David Sauzin (CNRS)
Introduction to resurgence on the example of saddle-node singularities (ENGLISH)
[ Abstract ]
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.
