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Invited talk

Wednesday, July 21, 14:45 ~ 15:45 UTC-3

The equivalence problem in analytic dynamics

Christiane Rousseau

University of Montreal, Canada   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

A central problem in local dynamics is the equivalence problem: when are two analytic systems locally equivalent under an analytic change of coordinates? In the neighbourhood of a singular point, representatives of equivalence classes could be given by normal forms. But, most often, the changes of coordinates to normal form diverge. Why? What does it mean? Unfolding the singularities reveals the geometric obstructions to the convergence to normal form. In this talk, we discuss a class of singularities and their unfoldings for which we can provide moduli spaces for the equivalence problems. We explain the common geometric features of these singularities, and how the study of the unfolding of these singularities allows understanding both the singularities themselves, and the obstructions to the existence of analytic changes of coordinates to normal form.

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