Name: Fractal Geometry and Number Theory (en Inglés)
SKU: 19201978
Price: 62350.00 CLP
Availability: InStock
Author: Michel L. Lapidus; Machiel Van Frankenhuysen
ISBN: 9780817640989

portada Fractal Geometry and Number Theory (en Inglés)

Fractal Geometry and Number Theory (en Inglés)

Formato

Libro Físico

Editorial

Birkhäuser

Autor

Michel L. Lapidus; Machiel Van Frankenhuysen

Año

1999

Idioma

Inglés

N° páginas

295

Encuadernación

Tapa Dura

Dimensiones

23.9x16.3x1.8 cm

Peso

0.57

ISBN

0817640983

ISBN13

9780817640989

N° edición

1999th

Categorías

Matemáticas aplicadas

Fractal Geometry and Number Theory (en Inglés)

Michel L. Lapidus; Machiel Van Frankenhuysen (Autor) · Birkhäuser · Tapa Dura

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Reseña del libro "Fractal Geometry and Number Theory (en Inglés)"

A fractal drum is a bounded open subset of R. m with a fractal boundary. A difficult problem is to describe the relationship between the shape (geo- metry) of the drum and its sound (its spectrum). In this book, we restrict ourselves to the one-dimensional case of fractal strings, and their higher dimensional analogues, fractal sprays. We develop a theory of complex di- mensions of a fractal string, and we study how these complex dimensions relate the geometry with the spectrum of the fractal string. We refer the reader to [Berrl-2, Lapl-4, LapPol-3, LapMal-2, HeLapl-2] and the ref- erences therein for further physical and mathematical motivations of this work. (Also see, in particular, Sections 7. 1, 10. 3 and 10. 4, along with Ap- pendix B. ) In Chapter 1, we introduce the basic object of our research, fractal strings (see [Lapl-3, LapPol-3, LapMal-2, HeLapl-2]). A 'standard fractal string' is a bounded open subset of the real line. Such a set is a disjoint union of open intervals, the lengths of which form a sequence which we assume to be infinite. Important information about the geometry of . c is contained in its geometric zeta function (c(8) = L lj. j=l 2 Introduction We assume throughout that this function has a suitable meromorphic ex- tension. The central notion of this book, the complex dimensions of a fractal string . c, is defined as the poles of the meromorphic extension of (c.