Transcendental dynamics and iterations on infinite-dimensional Teichmüller spaces – Konstantin Bogdanov

Konstantin Bogdanov
I2M, Aix-Marseille Université

Date(s) : 27/11/2020   iCal
11 h 00 min - 12 h 00 min

A task of high importance in holomorphic dynamics is to understand and describe the dynamical behavior of critical (or singular) orbits. The most famous example is the Mandelbrot set which parametrizes the set of quadratic polynomials with the non-escaping critical orbit. In our talk we present a theorem which classifies within certain families the transcendental entire functions for which all singular values escape, that is, inside of the complement of the “transcendental analogue” of the Mandelbrot set.

A key to the proof of this theorem is the generalization of the celebrated Thurston’s Topological Characterization of Rational Functions, but in our case we consider the infinite rather than finite post-singular set. Analogously to the Thurston’s theorem one defines the sigma-iteration on the Teichmüller space and investigates the question of convergence. But this time the underlying Teichmüller space is infinite-dimensional which leads to a completely different theory.

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