Fractal Geometry, Complex Dimensions and Zeta Functions
Fler böcker inom
Format
E-bok
Filformat
PDF med LCP-kryptering (0.0 MB)
Om LCP-kryptering
PDF-böcker lämpar sig inte för läsning på små skärmar, t ex mobiler.
Nedladdning
Kan laddas ned under 24 månader, dock max 6 gånger.
Språk
Engelska
Utgivningsdatum
2007-08-08
Förlag
Springer New York
ISBN
9780387352084

Fractal Geometry, Complex Dimensions and Zeta Functions E-bok

Geometry and Spectra of Fractal Strings

av Michel L Lapidus, Machiel Van Frankenhuijsen
E-bok (PDF, LCP),  Engelska, 2007-08-08
974
Ladda ned
Spara som favorit
Läs i Bokus Reader för iOS och Android
Finns även som
Visa alla 3 format & utgåvor
Number theory, spectral geometry, and fractal geometry are interlinked in this in-depth study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary.Key Features: - The Riemann hypothesis is given a natural geometric reformulation in the context of vibrating fractal strings- Complex dimensions of a fractal string, defined as the poles of an associated zeta function, are studied in detail, then used to understand the oscillations intrinsic to the corresponding fractal geometries and frequency spectra- Explicit formulas are extended to apply to the geometric, spectral, and dynamic zeta functions associated with a fractal- Examples of such formulas include Prime Orbit Theorem with error term for self-similar flows, and a tube formula- The method of diophantine approximation is used to study self-similar strings and flows- Analytical and geometric methods are used to obtain new results about the vertical distribution of zeros of number-theoretic and other zeta functionsThroughout new results are examined. The final chapter gives a new definition of fractality as the presence of nonreal complex dimensions with positive real parts.The significant studies and problems illuminated in this work may be used in a classroom setting at the graduate level. Fractal Geometry, Complex Dimensions and Zeta Functions will appeal to students and researchers in number theory, fractal geometry, dynamical systems, spectral geometry, and mathematical physics.
Visa hela texten

Kundrecensioner

Har du läst boken? Sätt ditt betyg »

Fler böcker av författarna

Michel L Lapidus, Machiel Van Frankenhuijsen

Du kanske gillar