Local holomorphic dynamics

seminar: On hedgehogs and dyamics of nonlinearizable holomorphic diffeomorphisms

speaker: Kingshook Biswas (Stony Brook)

abstract: The dynamics of a holomophic diffeomorphisms in the neighbourhood of an irrationally indifferent fixed point (a fixed point at which the derivative is of modulus one, but is not a root of unity) can be extremely complicated when the diffeomophism is nonlinearisable (ie cannot be conjugated to a rigid rotation around the fixed point) and much remains to be understood in this case. The geometric objects which play a central role in understanding the dynamics are a class of totally invariant connected compacts called 'hedgehogs', whose existence was established by Perez-Marco. In the nonlinearizable situation, one would like to think of hedgehogs as degenerate linearization domains; though one still doesn't have a rigorous mathematical formulation of this heuristic idea, I will describe results of Perez-Marco and myself which strongly support this point of view and show how fruitful it can be.

timetable:
Wed 24 Jan, 14:40 - 15:40, Aula Dini
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