%0 Thesis %A Silvestri, Stefano %D 2019 %T The Dynamics of Semigroups of Contraction Similarities on the Plane %U https://hammer.purdue.edu/articles/thesis/The_Dynamics_of_Semigroups_of_Contraction_Similarities_on_the_Plane/8953136 %R 10.25394/PGS.8953136.v1 %2 https://hammer.purdue.edu/ndownloader/files/16369973 %K Fractal Geometry %K Iterated Function Systems %K Complex Dynamics %K Mandelbrot Set %K Ordinary Differential Equations, Difference Equations and Dynamical Systems %K Pure Mathematics not elsewhere classified %K Mathematical Sciences not elsewhere classified %X
Given a parametrized family of Iterated Function System (IFS) we give sufficient conditions for a parameter on the boundary of the connectedness locus, M, to be accessible from the complement of M.
Moreover, we provide a few examples of such parameters and describe how they are connected to Misiurewicz parameter in the Mandelbrot set, i.e. the connectedness locus of the quadratic family z^2+c.
%I Purdue University Graduate School