Title: Local complex dimensions of a fractal string

Authors: Jacques Lévy Véhel; Franklin Mendivil

Addresses: INRIA, Regularity Team, Parc Orsay Université, 4 rue J. Monod, 91893 Orsay Cedex, France. ' Department of Mathematics and Statistics, Acadia University, Wolfville, NS, B4P 2R6, Canada

Abstract: We investigate in this work a local version of the theory of fractal strings and associated geometric zeta functions. Such a generalisation allows to describe the asymptotic behaviour of a 'fractal' set in the neighbourhood of any of its points. We give basic properties and several examples illustrating the possible range of situations concerning in particular the evolution of the local complex dimensions along the set and the relation between local and global zeta functions.

Keywords: fractal strings; complex dimensions; Minkowski measurability; Minkowski dimension; local box dimension; geometric zeta functions; fractals.

DOI: 10.1504/IJMMNO.2012.049603

International Journal of Mathematical Modelling and Numerical Optimisation, 2012 Vol.3 No.4, pp.281 - 297

Published online: 30 Aug 2014 *

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