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math.DS2019
Julia and Mandelbrot sets for dynamics over the hyperbolic numbers
Vance Blankers, Tristan Rendfrey, Aaron Shukert +1
Julia and Mandelbrot sets, which characterize bounded orbits in dynamical systems over the complex numbers, are classic examples of fractal sets. We investigate the analogs of thes…
math.DS2018
A fractal dimension for measures via persistent homology
Henry Adams, Manuchehr Aminian, Elin Farnell +6
We use persistent homology in order to define a family of fractal dimensions, denoted for each homological dimension , assigned to a proba…