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.
2006
Riemann surface; complex dynamics; branched covering; monodromy group; iterated monodromy group; Julia set; attractor; branch point; Riemann chaos; self-similar group; Green's function
01 Pubblicazione su rivista::01a Articolo in rivista
Fractal Riemann surfaces and their applications / Arrighetti, Walter. - In: COMMUNICATIONS TO SIMAI CONGRESS. - ISSN 1827-9015. - 1:(2006). [10.1685/CSC06012]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1656591
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