seminar: Some general methods in local holomorphic dynamics: Survey + Examples + Update.

speaker: Jean Ecalle ( CNRS (France) +Orsay University (France))

abstract: Local holomorphic dynamics seems to present a baffling, classification-defying variety of situations, but the root difficulties are, mercifully, few in number (mainly: "resonance", "quasiresonance","nihilence") and there exist for tackling them well-tried methods, which are often noticeable for their "algebraic" savour and high content in "structure". We shall attempt a quick survey of some of these methods : resurgence, acceleration, compensation, transseries, analysable functions, the bridge equation, mould calculus, arborification, etc. We shall then go through a series of classical examples, and wind up with more recent applications, which we feel shed new light on KAM theory (invariant tori, secular stability, Arnold diffusion). (Time may well be too short to cover all these topics, but we shall circulate a written summary of the talk.)

timetable:
Mon 22 Jan, 11:20 - 12:20, Aula Dini
documents:

ecalle.pdf

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