In holomorphic dynamics it is often important to understand the dynamical behaviour of critical (or singular) orbits. For quadratic polynomials, this leads to the study of the Mandelbrot set and of its complement. We present a classification of some explicit families of the transcendental entire functions for which all singular values escape, i.e. of the functions belonging to the complement of the "transcendental analogue" of the Mandelbrot set. A key ingredient in its proof is a generalisation of the famous Thurston's Topological Characterization of Rational Functions, but for the case of infinite rather than finite post-singular set. Analogously to Thurston's theorem, we consider a dynamical system in a specially chosen Teichmüller space and investigate its convergence. Unlike the classical case, the underlying Teichmüller space is infinite-dimensional which leads to completely different constructions.
Meeting ID: 852 4277 3200 Passcode: 103121