20 Maggio, 2016 14:30

Sezione di Geometria, Algebra e loro applicazioni

Repelling periodic points for transcendental entire functions

Anna Miriam Benini, Universita' di Roma Tor Vergata

Aula seminari del terzo piano

How many repelling periodic points of any period does a transcendental function have? For a generic rational function, the number of periodic points can be easily counted using the degree, and by the Fatou Shishikura inequality all but finitely many are repelling. Entire functions in general do not even need to have fixed points,see for example e^z+z. However we will be able to show-with a rather elementary proof- that for several important classes of transcendental functions there are-as expected-infinitely many repelling periodic points of any given period,and give some more information on the way they are distributed in the dynamical plane.