Local Connectivity of the Mandelbrot Set at Some Satellite Parameters of Bounded Type

We explore geometric properties of the Mandelbrot set $${{\mathcal {M}}}$$ , and corresponding Julia sets $${{\mathfrak {J}}}_c$$ near main cardioid. Namely, we establish that: (a) is locally connected at certain infinitely renormalizable parameters c bounded satellite type, providing first examples this kind; (b) The are also have positive area; (c) self-similar Siegel periodic type. approach these problems by analyzing unstable manifold pacman renormalization operator constructed authors jointly with N. Selinger in [DLS] as a global transcendental family. It occasion when external rays puzzles limiting maps applied to study Polynomial dynamics.