Fractal Riemann Surfaces and their Applications

Walter Arrighetti


Simple iterative ways to define Riemann surfaces with prescribed number of sheets and given branching via explicit equations are shown. The analysis is then focused on a class of Riemann surfaces analogue to IFS pre-fractals. Their topology (genus) and monodromy are closed-form computed; the associated self-similar symbolic dynamics is formalized and some convergence issues are presented. They are shown to serve as an interesting paradigm of chaos in some dynamical systems, used in Physics and Computer Science.

[DOI: 10.1685 / CSC06012] About DOI

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