Fractal Geometry, Complex Dimensions and Zeta Functions (Record no. 369453)

000 -LEADER
fixed length control field 05244nam a22005895i 4500
001 - CONTROL NUMBER
control field 978-0-387-35208-4
003 - CONTROL NUMBER IDENTIFIER
control field DE-He213
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20180115171402.0
007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION
fixed length control field cr nn 008mamaa
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 100301s2006 xxu| s |||| 0|eng d
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9780387352084
-- 978-0-387-35208-4
024 7# - OTHER STANDARD IDENTIFIER
Standard number or code 10.1007/978-0-387-35208-4
Source of number or code doi
050 #4 - LIBRARY OF CONGRESS CALL NUMBER
Classification number QA611-614.97
072 #7 - SUBJECT CATEGORY CODE
Subject category code PBP
Source bicssc
072 #7 - SUBJECT CATEGORY CODE
Subject category code MAT038000
Source bisacsh
082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 514
Edition number 23
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Lapidus, Michel L.
Relator term author.
245 10 - TITLE STATEMENT
Title Fractal Geometry, Complex Dimensions and Zeta Functions
Medium [electronic resource] :
Remainder of title Geometry and Spectra of Fractal Strings /
Statement of responsibility, etc. by Michel L. Lapidus, Machiel van Frankenhuijsen.
264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE
Place of production, publication, distribution, manufacture New York, NY :
Name of producer, publisher, distributor, manufacturer Springer New York,
Date of production, publication, distribution, manufacture, or copyright notice 2006.
300 ## - PHYSICAL DESCRIPTION
Extent XXIV, 460 p. 54 illus.
Other physical details online resource.
336 ## - CONTENT TYPE
Content type term text
Content type code txt
Source rdacontent
337 ## - MEDIA TYPE
Media type term computer
Media type code c
Source rdamedia
338 ## - CARRIER TYPE
Carrier type term online resource
Carrier type code cr
Source rdacarrier
347 ## - DIGITAL FILE CHARACTERISTICS
File type text file
Encoding format PDF
Source rda
490 1# - SERIES STATEMENT
Series statement Springer Monographs in Mathematics,
International Standard Serial Number 1439-7382
505 0# - FORMATTED CONTENTS NOTE
Formatted contents note Complex Dimensions of Ordinary Fractal Strings -- Complex Dimensions of Self-Similar Fractal Strings -- Complex Dimensions of Nonlattice Self-Similar Strings: Quasiperiodic Patterns and Diophantine Approximation -- Generalized Fractal Strings Viewed as Measures -- Explicit Formulas for Generalized Fractal Strings -- The Geometry and the Spectrum of Fractal Strings -- Periodic Orbits of Self-Similar Flows -- Tubular Neighborhoods and Minkowski Measurability -- The Riemann Hypothesis and Inverse Spectral Problems -- Generalized Cantor Strings and their Oscillations -- The Critical Zeros of Zeta Functions -- Concluding Comments, Open Problems, and Perspectives.
520 ## - SUMMARY, ETC.
Summary, etc. 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 dynamical zeta functions associated with a fractal Examples of such explicit formulas include a Prime Orbit Theorem with error term for self-similar flows, and a geometric 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 functions Throughout new results are examined. The final chapter gives a new definition of fractality as the presence of nonreal complex dimensions with positive real parts, and discusses several open problems and extensions. 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. From Reviews of Fractal Geometry and Number Theory: Complex Dimensions of Fractal Strings and Zeros of Zeta Functions, by Michel Lapidus and Machiel van Frankenhuysen, Birkhäuser Boston Inc., 2000. "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 "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.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Mathematics.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Dynamics.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Ergodic theory.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Global analysis (Mathematics).
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Manifolds (Mathematics).
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Measure theory.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Partial differential equations.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Number theory.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Topology.
650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Mathematics.
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Topology.
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Number Theory.
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Measure and Integration.
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Partial Differential Equations.
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Dynamical Systems and Ergodic Theory.
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Global Analysis and Analysis on Manifolds.
700 1# - ADDED ENTRY--PERSONAL NAME
Personal name Frankenhuijsen, Machiel van.
Relator term author.
710 2# - ADDED ENTRY--CORPORATE NAME
Corporate name or jurisdiction name as entry element SpringerLink (Online service)
773 0# - HOST ITEM ENTRY
Title Springer eBooks
776 08 - ADDITIONAL PHYSICAL FORM ENTRY
Relationship information Printed edition:
International Standard Book Number 9780387332857
830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE
Uniform title Springer Monographs in Mathematics,
International Standard Serial Number 1439-7382
856 40 - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier <a href="http://dx.doi.org/10.1007/978-0-387-35208-4">http://dx.doi.org/10.1007/978-0-387-35208-4</a>
912 ## -
-- ZDB-2-SMA
Holdings
Withdrawn status Lost status Damaged status Not for loan Collection code Permanent Location Current Location Date acquired Date last seen Price effective from Koha item type
  Not Lost     EBook e-Library e-Library 2018-01-15 2018-01-15 2018-01-15 eBook

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