In this paper a family of compact Riemann surfaces are syntesized whose branching and iterated monodromy is shown to be prefractal in the sense of self-similar groups. The surfaces are defined via iteration of polynomial or rational functions whereas the complex dynamics on their multivalued Julia sets show some degree of chaotic behaviour. Application of these surfaces to spectral-domain electrodynamic problems in heterogeneous media is then set.
Fractal Riemann surfaces and their applications / Arrighetti, Walter. - In: COMMUNICATIONS TO SIMAI CONGRESS. - ISSN 1827-9015. - 1:(2006). [10.1685/CSC06012]
Fractal Riemann surfaces and their applications
Arrighetti, Walter
2006
Abstract
In this paper a family of compact Riemann surfaces are syntesized whose branching and iterated monodromy is shown to be prefractal in the sense of self-similar groups. The surfaces are defined via iteration of polynomial or rational functions whereas the complex dynamics on their multivalued Julia sets show some degree of chaotic behaviour. Application of these surfaces to spectral-domain electrodynamic problems in heterogeneous media is then set.File allegati a questo prodotto
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