Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 43, 2018, 835-857

THICK SELF SIMILAR SETS ARE ASYMPTOTICALLY GENERIC

Driss Essouabri and Ben Lichtin

Univ. Lyon, UJM-Saint-Etienne, CNRS, Institut Camille Jordan UMR 5208
Faculté des Sciences et Techniques, 23 rue du Docteur Paul Michelon
F-42023, Saint-Etienne, France; driss.essouabri 'at' univ-st-etienne.fr

lichtin 'at' frontier.com

Abstract. This paper studies the property of thickness for a class of self-similar sets that satisfy a non overlapping condition introduced by Strichartz. We show that in a suitable sense thickness is a generic property.

2010 Mathematics Subject Classification: Primary 11M41, 28A80, 52C10, 11J69, 11M32.

Key words: Self-similar discrete sets, fractals, zeta functions, meromorphic continuation, n-simplices in fractals.

Reference to this article: D. Essouabri and B. Lichtin: Thick self similar sets are asymptotically generic. Ann. Acad. Sci. Fenn. Math. 43 (2018), 835-857.

Full document as PDF file

https://doi.org/10.5186/aasfm.2018.4349