Toward zeta functions and complex dimensions of multifractals

Details Toward zeta functions and complex dimensions of multifractals Toward zeta functions and complex dimensions of multifractals

2008-10-04

arxiv.org/abs/0810.0789v1

Physics

Mathematical Physics

16 pages, 6 figures. This paper has been accepted for publication in the journal Complex Variables and Elliptic Equations

Scientific paper

Multifractals are inhomogeneous measures (or functions) which are typically described by a full spectrum of real dimensions, as opposed to a single real dimension. Results from the study of fractal strings in the analysis of their geometry, spectra and dynamics via certain zeta functions and their poles (the complex dimensions) are used in this text as a springboard to define similar tools fit for the study of multifractals such as the binomial measure. The goal of this work is to shine light on new ideas and perspectives rather than to summarize a coherent theory. Progress has been made which connects these new perspectives to and expands upon classical results, leading to a healthy variety of natural and interesting questions for further investigation and elaboration.

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