Fractal Geometry and Number Theory
Language: English
Published by Birkhäuser, 1999
- Softcover
- New
Seller: Agapea Libros, Malaga, MA, SpainAgapea Libros
AbeBooks seller since September 15, 2009
Condition: New
£ 45.42
Quantity: 2 available
Add to basketItem description from seller
Idioma/Language: 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. *** Nota: Los envíos a España peninsular, Baleares y Canarias se realizan a través de mensajería urgente. No aceptamos pedidos con destino a Ceuta y Melilla.…
Seller Inventory # 888761
- Title
- Fractal Geometry and Number Theory
- Author
- Lapidus, Michel L.; van Frankenhuysen, Machiel
- Publisher
- Birkhäuser
- Publication year
- 1999
- Condition
- New
- Binding
- Soft cover
- Language
- English
- ISBN 10
- 0817640983
- ISBN 13
- 9780817640989
- Item weight
- 589 grams
- Seller catalogs
- Álgebra
"Synopsis" may belong to another edition of this title.
Review
"This highly original self-contained book will appeal to geometers, fractalists, mathematical physicists and number theorists, as well as to graduate students in these fields and others interested in gaining insight into these rich areas either for its own sake or with a view to applications. They will find it a stimulating guide, well written in a clear and pleasant style."
–Mathematical Reviews (Review of First Edition)
"It is the reviewer’s opinion that the authors have succeeded in showing that the complex dimensions provide a very natural and unifying mathematical framework for investigating the oscillations in the geometry and the spectrum of a fractal string. The book is well written. The exposition is self-contained, intelligent and well paced."
–Bulletin of the London Mathematical Society (Review of First Edition)
"The new approach and results on the important problems illuminated in this work will appeal to researchers and graduate students in number theory, fractal geometry, dynamical systems, spectral geometry, and mathematical physics."
–Simulation News Europe (Review of First Edition)
"About the title" may belong to another edition of this title.
Agapea Libros
Malaga, MA, Spain
AbeBooks seller since September 15, 2009
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