One-parameter semigroups of holomorphic self-maps of the unit disc: speeds of convergence and asymptotic behaviour
speaker: Filippo Bracci (Università di Roma 'Tor Vergata')abstract: In this talk I will survey some recent results on the dynamics of continuous one-parameter semigroups of holomorphic self-maps of the unit disc. In particular I will concentrate on the case of non-elliptic semigroups. In such a case, the orbits converge to a boundary point, called the Denjoy-Wolff point. The most interesting questions are about the type and speed of convergence (tangentialnon-tangentialoscillating…). In order to study those questions, some years ago I introduced three “speeds” (total, orthogonal and tangential), which can be used to understand the behaviour of the orbits. Those speeds can be studied via hyperbolic theory, Gromov hyperbolicity theory and harmonic measure theory. In this talk I will give a summary of the results in this context and present some ideas underlying.
timetable:
Fri 31 May, 9:00 - 9:50, Aula Dini
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