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SIMBa: The escape trichotomy for singularly perturbed polynomials

SIBMa

El proper dimecres, 21 de novembre, se celebrarà una nova xerrada del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Speaker: Dan Alexandru Paraschiv
Universitat: Universitat de Barcelona

Data: Dimecres, 21 de novembre de 2018
Hora: 12:00, cafè; 12:20, xerrada
Lloc: Aula B1 Facultat de Matemàtiques de la Universitat de Barcelona.
Idioma: English

Títol: The escape trichotomy for singularly perturbed polynomials
Resum: Holomorphic dynamics studies the iteration of holomorphic functions over different spaces.
The dichotomy for quadratic polynomials, which generates the Mandelbrot set, is one of the fundamental results.
Devaney, Look and Uminsky have managed to extend this result to the family of singularly perturbed polynomials, that is: F_{\lambda}(z)=z^{n}+\frac{\lambda}{z^d}, where \lambda \in \mathbb{C}, z \in \hat{\mathbb{C}},n, d \in \mathbb{N^*} and d \geq 2.
The scape trichotomy shows that, according to the position of the critical values of the map, there exist 3 possible kinds of Julia sets: Cantor sets, Cantor sets of quasicircles and Sierpinski curves. For a clear understanding of the result, there are first going to be presented several basic notions and results from holomorphic dynamics.

Si voleu estar al cas de les xerrades previstes, podeu consultar el calendari. Si voleu proposar una xerrada, ompliu el formulari. Si voleu contactar amb els responsables podeu escriure un missatge a seminari(dot)simba(at)ub(dot)edu.