Fractal Riemann Surfaces: Chaotic Scenarios and Applications

Auteurs-es

  • Walter Arrighetti “Sapienza” Università di Roma; TECHNICOLOR Creative Services

DOI :

https://doi.org/10.1685/

Mots-clés :

Fractal Riemann surface, Riemann surface, branched cover, branch point, sheet, self-similarity, fractal dimension, surface genus, homotopy group, monodromy group, IMG, iterated monodromy group, symbolic dynamics, pre-fractal, Galois Theory, cryptography

Résumé

Fractal Riemann surfaces are generated as iterators of branched covers (complex multi-valued functions). They feature self-similar geometries, an interesting Iterated Monodromy Group driving their topologies, and an easy way to get their symbolic dynamics browsed. On the contrary, convergence issues, numerical accuracy and the onset of chaotic dynamics are present in the direct, homotopy problem of computing paths on them. Theoretical results of analysis and synthesis will be given, with hints to possible applications in Computer Science (signing and private-key cryptography) and Physics (direct and inverse scattering from fractal objects). [DOI: 10.1685/CSC09313] About DOI

Biographie de l'auteur-e

  • Walter Arrighetti, “Sapienza” Università di Roma; TECHNICOLOR Creative Services
    TECHNICOLOR S.p.A. Creative Service Engineer PhD in Electromagnetism

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Publié

2009-08-12

Numéro

Vol. 3 (2009)

Rubrique

Articles

Licence

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