Holomorphic day 2022

On July 25 we organize a workshop in holomorphic dynamics at IMUB's Seminar Room. The workshop will consist on several talks and it will coincide with the last session of the seminar (course 21-22).

Next course we will start the seminar by the end of September.

If you are interested in attending the workshop please contact us: xavier.jarque AT ub.edu.


  Speaker Institution Title
10.00-10.30 Àlex Rodríguez Universitat de Barcelona Surgery on a family of transcendental meromorphic maps
10.30-11.00 Anna Jové Universitat de Barcelona Dynamics on the boundary of Fatou components
11.00-11.30 Coffee break    
11.30-12.00 Robert Florido Universitat de Barcelona Quasiperiodically forced quadratic maps
12.00-13.00          Leticia Pardo Manchester University

The maximum modulus set of an entire function


Surgery on a family of transcendental meromorphic maps: In this talk a surgery process applied to a meromorphic map is explained. The main result is that the Julia set of some functions in this family contains a Cantor bouquet (a homeomorphic copy of the Julia set of an exponential map). The proof requieres to interpolate in an unbounded domain.

Dynamics on the boundary of Fatou components: In this talk, we will review some known results about boundary dynamics in invariant Fatou components of transcendental entire functions. Moreover, we will present new conditions which implies that periodic boundary points and escaping boundary points are dense in the boundary. Finally, we will discuss a particular case of Siegel disks of transcendental entire functions which have no periodic boundary points.

Quasiperiodically forced quadratic maps: Quasiperiodically forced maps are a special class of skew-products over an irrational rotation. Their complexification as fibered holomorphic maps has been investigated by Ponce, analyzing their local dynamics around invariant curves and complementing the work of Sester on fibered Julia sets in the polynomial case. We study a family of quasiperiodically forced quadratic maps, which includes Ponce’s example admitting two attracting invariant curves, a phenomenon that cannot occur in the non-fibered setting.

The maximum modulus set of an entire function: The set of points where an entire function achieves its maximum modulus is known as the maximum modulus set, and usually consists of a collection of disjoint analytic curves. In this talk, we discuss recent progress on the description of the features that this set might exhibit. Namely, on the existence of discontinuities, singleton components, and on its structure near the origin. Time permitted, I will also comment on work in progress on a question of Erdos. This is based on joint work with D. Sixsmith, V. Evdoridou and A. Glücksam.