# Singular values and nonrepelling cycles

- Date:
- 26.05.20
- Times:
- 15:30 to 16:30
- Place:
- on-line
- Speaker:
- Anna Miriam Benini
- University:
- Universita di Parma

#### Abstract

We will focus on the mutual relations between singular values,

periodic rays and periodic orbits in transcendental dynamics.

It is classically known that the existence of non-repelling periodic

points is connected to the presence of a singular value 'near by'- for

example, attracting and parabolic basins need to contain at least one

singular value. For repelling periodic points, singular values come

into play when the periodic point in question is not the landing point

of any periodic ray.

In this talk we will show that under our assumptions, it is possible

to associate a specific singular orbit to every non-repelling cycle,

as well as to every repelling cycle whose points are not landing

points of periodic rays.

This gives a version of the Fatou-Shishikura inequality which takes

into account such repelling cycles.

This is joint work with N. Fagella.