Dynamical Systems

Seminar for graduate/PhD students at the University of Warsaw and all researches interested in Dynamical Systems


Academic year 2023/24


Winter semester
Date
Speaker
Title
Abstract
6.10.2023

Presentation of the scope of the seminar, setting programme for the winter semester

13.10.2023
Julia Ścisłowska
Julia sets for holomorphic maps – basic properties. Part I

20.10.2023
Juliusz Pham
Julia sets for holomorphic maps – basic properties. Part II

27.10.2023
Igor Buchowiec
Local behaviour of a holomorhic map near an attracting fixed point

30.10.2023
Krzysztof Barański
Dense images of straight lines under exopential iteration

10.11.2023
Ilona Płachecka
Local behaviour of a holomorhic map near a rationally neutral point

17.11.2023
Maciej Białobrzeski
Local behaviour of a holomorhic map near an irrationally neutral point

24.11.2023
Juliusz Pham
Classification theorem for Fatou components. Part I

1.12.2023
Juliusz Pham
Classification theorem for Fatou components. Part II

8.12.2023
Julia Ścisłowska
Critical points and dynamics of the map. Hyperbolic Julia sets

15.12.2023
Ilona Płachecka
Quadratic family – Mandelbrot set, bifurcations

12.01.2024
Leticia Pardo-Simón (University of Manchester)
Constructing entire functions with wandering domains
Let $f$ be a transcendental entire function, that is, a non-polynomial holomorphic self-map of the complex plane. Transcendental dynamics studies what happens to a point z under repeated iteration of the function $f$. In particular, points might belong to wandering domains, that is, open ‘maximal’ regions of stability whose images under iteration are all disjoint from each other. In this talk I will discuss how recent techniques based on approximation theory allow us to construct a wide range of examples: from wandering domains that remain in a bounded part of the plane for ‘almost all’ iterates to those that converge to infinity ‘as fast as possible’. This is based on joint work with A. Glücksam, V. Evdoridou and D. Sixsmith.
19.01.2024
Igor Buchowiec
Newton's method for finding roots of holomorphis functions

26.01.2024
Radosław Opoka
Complex exponential family – topological and geometric properties of Julia sets



Summer semester
Date
Speaker
Title
Abstract
1.03.2024
Joanna Horbaczewska
Complex exponential family – dimension paradox

8.03.2024

Setting programme for the summer semester

15.03.2024
Łukasz Pawelec (IMPAN)
Dimension paradox in parameter plane for exponential family

22.03.2024
Radosław Opoka
On entire maps from Eremenko-Lyubich class. Part I

27.03.2024
Maciej Białobrzeski
On entire maps from Eremenko-Lyubich class. Part II

5.04.2024
Joanna Horbaczewska
Hyperbolic dimension of Julia sets of meromorphic maps with logarithmic tracts

12.04.2024
Igor Buchowiec
Wandering domains of entire maps. Part I

19.04.2024
Igor Buchowiec
Wandering domains of entire maps. Part II

26.04.2024
Juliusz Pham
Dynamics of inner functions. Part I

6.05.2024
Krzysztof Barański
Dynamics of inner functions

17.05.2024
Julia Ścisłowska
Continua in transcendental dynamics. Part I

24.05.2024
Julia Ścisłowska
Continua in transcendental dynamics. Part II

7.06.2024
Juliusz Pham
Dynamics of inner functions. Part II

14.06.2024
Maciej Białobrzeski
Dynamics of inner functions. Part III