Complex Dimensions of Self-Similar Fractal Strings and Diophantine Approximation

DOI10.1080/10586458.2003.10504711zbMath1061.11039OpenAlexW2021668178MaRDI QIDQ4811490

Michel L. Lapidus, Machiel van Frankenhuijsen

Publication date: 6 September 2004

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.em/1064858783

zbMATH Keywords

diophantine approximationcomplex fractal dimensionDirichlet polynomial equationsself-similar strings

Mathematics Subject Classification ID

Other Dirichlet series and zeta functions (11M41) Fractals (28A80) Dimension theory of smooth dynamical systems (37C45) Diophantine approximation in probabilistic number theory (11K60) Diophantine approximation, transcendental number theory (11J99)

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Fractal strings and multifractal zeta functions ⋮ Zeta functions and solutions of Falconer-type problems for self-similar subsets of ℤⁿ ⋮ Fourier frequencies in affine iterated function systems ⋮ Domain of meromorphy of a class of Bateman-like totient zeta functions ⋮ On the Complex Dimensions of Nonlattice Fractal Strings in Connection with Dirichlet Polynomials ⋮ Pointwise tube formulas for fractal sprays and self-similar tilings with arbitrary generators ⋮ Extremal problems in the Fock space ⋮ Tube formulas and complex dimensions of self-similar tilings ⋮ An overview of complex fractal dimensions: from fractal strings to fractal drums, and back ⋮ On the existence of fractal strings whose set of dimensions of fractality is not perfect

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