Event Details
Title: Wandering domains in holomorphic dynamics
Conferenciante: Xavier Jarque (Universitat de Barcelona)
Abstract: Iteration of holomorphic maps in the complex plane has been an interesting piece of dynamical systems during the last 40 years. The main ideas introduced by Fatou and Julia around 1930 were (almost) forgotten for more than 40 years until some authors were attracted by the Mandelbrot set. Right after, some people start to work on the iteration of transcendental functions. In this talk I will concentrate in the transcendental entire case and the existence (and non-existence) of wandering domains (that is, domains of the Fatou set which are not eventually periodic). From the celebrated Sullivan's Theorem on the non-existence of those domains for rational maps, until recent results by C. Bishop on the existence of wandering domains in Eremenko-Lyubich class (a class of transcendental entire maps). I'll present the main results and partially discuss some of the key ingredients in the arguments of the proofs.
13 de enero de 2016, 12:45, Seminario 1ª planta IEMath-GR
Más información sobre el seminario de ecuaciones diferenciales aquí.
Conferenciante: Xavier Jarque (Universitat de Barcelona)
Abstract: Iteration of holomorphic maps in the complex plane has been an interesting piece of dynamical systems during the last 40 years. The main ideas introduced by Fatou and Julia around 1930 were (almost) forgotten for more than 40 years until some authors were attracted by the Mandelbrot set. Right after, some people start to work on the iteration of transcendental functions. In this talk I will concentrate in the transcendental entire case and the existence (and non-existence) of wandering domains (that is, domains of the Fatou set which are not eventually periodic). From the celebrated Sullivan's Theorem on the non-existence of those domains for rational maps, until recent results by C. Bishop on the existence of wandering domains in Eremenko-Lyubich class (a class of transcendental entire maps). I'll present the main results and partially discuss some of the key ingredients in the arguments of the proofs.
13 de enero de 2016, 12:45, Seminario 1ª planta IEMath-GR
Más información sobre el seminario de ecuaciones diferenciales aquí.
