Parabolic renormalization

Glocal objects in complex dynamical systems

speaker: Loïc TEYSSIER (Université de Strasbourg)

abstract: A \(glocal\) dynamical system is a germ of a dynamical system in the heighborhood of a point in an affine space which is the expression of a global (i.e. on a compact surface) dynamical system in some local chart. A long standing open question regards how to characterize glocal dynamical system. \[\] I'll investigate this issue in the context of complex holomorphic dynamics both in the case of a parabolic unidimensional diffeomorphism, and in the case of a saddle-node foliation in \(\mathbb C^2\). Those objects are linked through the holonomy representation of the foliation, and share the same classifying horn map. I'll try to present radically different tracks and frameworks leading to partial characterizations, with the (yet unreached) aim of describing a non-glocal differential equation. The existence of such equations has been established recently but no «explicit» example has been produced so far.

timetable:
Thu 6 Jun, 11:00 - 12:00, Sala Conferenze Centro De Giorgi
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