Spectral zeta functions of fractals and the complex dynamics of polynomials

DOI10.1090/S0002-9947-07-04150-5zbMath1129.28010arXivmath/0505546OpenAlexW2032481310MaRDI QIDQ3443134

Alexander Teplyaev

Publication date: 31 May 2007

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0505546

zbMATH Keywords

Laplacianfractalspectral zeta functionfractal stringrational complex dynamics

Mathematics Subject Classification ID

Unimodular groups, congruence subgroups (group-theoretic aspects) (20H05) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Spectrum, resolvent (47A10) Ergodic theorems, spectral theory, Markov operators (37A30) Fractals (28A80) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Spectral theory; eigenvalue problems on manifolds (58C40)

Related Items (23)

Spectral decimation of a self-similar version of almost Mathieu-type operators ⋮ Regularized Laplacian determinants of self-similar fractals ⋮ Complex dimensions of fractals and meromorphic extensions of fractal zeta functions ⋮ Existence of a meromorphic extension of spectral zeta functions on fractals ⋮ Towards quantized number theory: spectral operators and an asymmetric criterion for the Riemann hypothesis ⋮ Multifractional theories: an unconventional review ⋮ Spectral decimation of piecewise centrosymmetric Jacobi operators on graphs ⋮ Dirac and magnetic Schrödinger operators on fractals ⋮ Complex asymptotics of Poincaré functions and properties of Julia sets ⋮ Truncated infinitesimal shifts, spectral operators and quantized universality of the Riemann zeta function ⋮ Distance and tube zeta functions of fractals and arbitrary compact sets ⋮ Random Walks on Barycentric Subdivisions and the Strichartz Hexacarpet ⋮ Wave equation on one-dimensional fractals with spectral decimation and the complex dynamics of polynomials ⋮ Fractal zeta functions and complex dimensions of relative fractal drums ⋮ Geometry and field theory in multi-fractional spacetime ⋮ Breaking of continuous scale invariance to discrete scale invariance: a universal quantum phase transition ⋮ Expansion in generalized eigenfunctions for Laplacians on graphs and metric measure spaces ⋮ VIBRATION SPECTRA OF FINITELY RAMIFIED, SYMMETRIC FRACTALS ⋮ Poincaré Functional Equations, Harmonic Measures on Julia Sets, and Fractal Zeta Functions ⋮ Fractal Zeta Functions and Complex Dimensions: A General Higher-Dimensional Theory ⋮ Singularly continuous spectrum of a self-similar Laplacian on the half-line ⋮ Gaps in the spectrum of the Laplacian on \(3N\)-gaskets ⋮ An overview of complex fractal dimensions: from fractal strings to fractal drums, and back

Cites Work

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