BSU Mathematics Seminar
Rigorous Estimation of Hausdorff Dimensions for Continued Fraction Iterated Function Systems
Speaker: Jacob Brown, University of Connecticut
Abstract
In this talk, we will discuss a method for the rigorous estimation of Hausdorff dimensions of limit sets produced by continued fraction iterated function systems. The method is based on the approximation of a Perron-Frobenius operator using the finite element method with B-splines as the choice of basis functions. We will see that this method provides several key numerical advantages over other methods, such as higher-order convergence and increased computational flexibility. We will discuss numerical results to verify both the rigor and higher-order convergence of our method for quadratic B-spline interpolants in one and two dimensions.
Speaker
Jacob Brown is a fourth-year PhD candidate in the Mathematics department at the University of Connecticut. His research lies in the intersection of numerical analysis and dynamical systems, using the finite element method to rigorously estimate the Hausdorff dimensions of fractals produced by conformal iterated function systems.
Jacob is also very passionate about his teaching, and in his free time, he enjoys reading and writing short stories.