# Dynamics Seminar

Event Information Boundary of the Mandelbrot set for a pair of linear maps
15:10 on Monday February 25, 2019
16:00 on Monday February 25, 2019
BA6183, Bahen Center, 40 St. George St.
Stefano Silverstri

IUPUI

Consider two objects associated to the IFS $\{\lambda z+1,\lambda z-1\}$ : the locus $\mathcal{M}$ of parameters $\lambda\in\mathbb{D}\setminus 0$ for which the corresponding attractor is connected; an the locus $\mathcal{M}_0$ of parameters for which the related attractor contains 0. The set $\mathcal{M}$ can also be characterized as the locus of parameters for which the attractor of the IFS $\{\lambda z+1, \lambda z, \lambda z-1\}$ contains 0. Exploiting the asymptotic similarity of $\mathcal{M}$ and $\mathcal{M}_0$ with the respective associated attractors, I give sufficient conditions on $\lambda\in\partial\mathcal{M}$ or $\partial\mathcal{M}_0$ to guarantee it is accessible (not buried). Moreover, for a specific parameter $\lambda\in\partial\mathcal{M}$ I will describe the method used to show it is accessible from the largest connected component of $\mathbb{D}\setminus\mathcal{M}$.