Hi! I'm Víctor Álvarez Aparicio, math and scientific programming enthusiast. I'm currently working as a research fellow in University of La Rioja (Spain), studying applications of Topology in the field of Iteration of Rational Maps and Complex Dynamics. My colleagues and I mainly develop our algorithms in Julia Language.
My interests are Algebraic Topology, Differential Topology, Complex Dynamics and Ergodic Theory, Iterative Proccesses, Scientific Programming, Julia Language, TDA (Topological Data Analysis), among others. I'm really glad and excited to join this community and to share our contributions with everyone interested!
We present a new collection of algorithms dedicated to compute the basins of attraction of any complex rational map. This is a relevant matter in Holomorphic Dynamics, and also a way to visualize and study amazing fractal objects like Julia Sets. These algorithms solve many computational problems that often arise in Numerical Analysis, like overflows or mathematical indeterminations, and provide more information about the dynamics of the system than traditional algorithms generally do.