The talks take place on Thursdays at 12:15 (BCN time, CET) at IMUB (Universitat de Barcelona).

**Coming talks**

**November 24, 2023, 14:00**(Universitat de Barcelona)This email address is being protected from spambots. You need JavaScript enabled to view it.

T**itle:**Local connectivity of boundaries of Fatou components III**Abstract:**In the talk, I will re-prove the famous result of Roesch and Yin about local connectivity of boundaries of bounded Fatou components of polynomials (except Siegel). For this, I will present techniques of puzzles and generalized renormalizations (box mappings) and will show how to use these techniques to get the result. All necessary background will be provided.

**Past talks (2023/24)**

**November 16, 2023, 12:15**(Universitat de Barcelona)This email address is being protected from spambots. You need JavaScript enabled to view it.

T**itle:**Local connectivity of boundaries of Fatou components II**Abstract:**In the talk, I will re-prove the famous result of Roesch and Yin about local connectivity of boundaries of bounded Fatou components of polynomials (except Siegel). For this, I will present techniques of puzzles and generalized renormalizations (box mappings) and will show how to use these techniques to get the result. All necessary background will be provided.**November 10, 2023, 14:00**(Universitat de Barcelona)This email address is being protected from spambots. You need JavaScript enabled to view it.

T**itle:**Local connectivity of boundaries of Fatou components**Abstract:**In the talk, I will re-prove the famous result of Roesch and Yin about local connectivity of boundaries of bounded Fatou components of polynomials (except Siegel). For this, I will present techniques of puzzles and generalized renormalizations (box mappings) and will show how to use these techniques to get the result. All necessary background will be provided.**November 2, 2023, 12:15**(University of Warsaw)This email address is being protected from spambots. You need JavaScript enabled to view it.

T**itle:**Local connectivity of the boundary of a Fatou component**Abstract:**In this talk I will present my current work on local conectivity of the boundary of the Baker Domain of the function $f(x)=z-\frac{1-e^z}{1-2e^z}$ ($N((e^z)(1-e^z))$).**October 26, 2023, 12:15**(Centre de Recerca Matemàtica)**Gustavo Rodrigues Ferreira**

T**itle:**Transcendental dynamics and wandering domains III **Abstract:**In this three-part talk, we will discuss the internal dynamics of wandering domains of meromorphic functions. Focusing on the hyperbolic distance between pairs of orbits, we will show that every wandering of a meromorphic function locally resembles a wandering of an entire function.**October 19, 2023, 12:15**(Universitat de Barcelona)**Xavier Jarque i Ribera**

T**itle:**Connectivity of the basins of attraction of fixed points for some root finding algorithms**Abstract:**We consider the connectivity of the immediate basins of attraction for different dynamical systems, basically inspired by root-finding algorithms, as the title already explains.**October 16, 2023, 12:00**(Indiana University)**Kevin Pilgrim**

T**itle:**Real bimodal quadratic rational maps: moduli space and entropyBruin-van Strien and Kozlovski showed that for multimodal self-maps $f$ of the unit interval, the function $f \mapsto h(f)$ sending $f$ to its topological entropy is monotone. K. Filom and I showed that for interval maps arising from real bimodal quadratic rational maps, this monotonicity fails. A key ingredient in our proof is an analysis of a family $f_{p/q}, p/q \in \mathbb{Q}/\mathbb{Z}$ of critically finite maps on which the dynamics on the postcritical set is conjugate to the rotation $x \mapsto x+p \bmod q$ on $\mathbb{Z}/q\mathbb{Z}$, where $x=0$ and $x=1$ correspond to the two critical points. The recent PhD thesis of S. Kang constructs a piecewise-linear (PL) copy of the well-known Farey tree whose vertices are expanding PL quotients of the $f_{p/q}$’s. This PL model, conjecturally, sheds light on the moduli space of the real quadratic bimodal family, and on the variation of entropy among such maps.

Abstract:(Joint work with K. Filom and S. Kang)

**October 5, 2023, 12:15**(Tel Aviv University)**Oleg Ivrii**

T**itle:**Pesin theory and inner functionsAn inner function is a holomorphic self-map of the unit disk which extends to a measure-theoretic dynamical system of the unit circle. Even though the forward dynamics of an inner function can be very wild, if its derivative belongs to the Nevanlinna class, then backward iteration is asymptotically linear along almost every inverse orbit. We give several applications.

Abstract:

(This is joint work with Mariusz Urbański.)**September 28, 2023, 12:30**(Centre de Recerca Matemàticaa)**Gustavo Rodrigues Ferreira**

T**itle:**Transcendental dynamics and wandering domains II **Abstract:**In this three-part talk, we will discuss the internal dynamics of wandering domains of meromorphic functions. Focusing on the hyperbolic distance between pairs of orbits, we will show that every wandering of a meromorphic function locally resembles a wandering of an entire function.**September 21, 2023, 12:30**(Centre de Recerca Matemàtica)**Gustavo Rodrigues Ferreira**

T**itle:**Transcendental dynamics and wandering domains **Abstract:**In this three-part talk, we will discuss the internal dynamics of wandering domains of meromorphic functions. Focusing on the hyperbolic distance between pairs of orbits, we will show that every wandering of a meromorphic function locally resembles a wandering of an entire function.