Topological and Combinatorial Problems in One-dimensional Complex Dynamics
timetable:
Thu 17 Oct, 15:45 - 16:15, Aula Dini
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Singular values and bounded Siegel Disks
speaker: Anna Miriam Benini (Centro di Ricerca Matematica "Ennio De Giorgi")abstract: Let $f$ be an entire transcendental function and $\Delta$ be a forward invariant bounded Siegel disk for $f$ with rotation number in Herman's class $\HH$. We show that if $f$ belongs to a certain wide class of entire functions, the boundary of $\Delta$ contains a critical point, provided that there are only two singular values interacting with the Siegel disk. We also prove several general results on the mapping properties of entire functions and on the relation between preimages of sets and the presence of singular values. These include a weak form of Ma\~n\'e's Theorem according to which the boundary of a bounded Siegel disk must be accumulated by the orbit of a recurrent critical point.
timetable:
Thu 17 Oct, 15:45 - 16:15, Aula Dini
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