Taming the elephants in the Mandelbrot set

par Carsten Petersen (Roskilde University)

vendredi 29 sept. 2023, 10:30 → 11:30 Europe/Paris

207 (Bat 1R2)

We study classes of transcendental Horn and Adam maps, which contain the classical horn maps and their quotients coming from the dynamics on simple parabolic basins such as $z^2+1/4$ on the Cauliflower.
We define and describe the structure of the dynamical and parameter “lagoa rays” and use these rays to design the Yoccoz puzzle machinery in this setting. As a first consequence, we obtain the precise asymptotics of secondary satellite copies of “principal elephants” near the cusp of the Mandelbrot set.