MARC details
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03240nam a22005655i 4500 |
| 001 - CONTROL NUMBER |
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| control field |
978-0-8176-4727-8 |
| 003 - CONTROL NUMBER IDENTIFIER |
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| control field |
DE-He213 |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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| control field |
20180115171439.0 |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION |
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| fixed length control field |
cr nn 008mamaa |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
100301s2009 xxu| s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9780817647278 |
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978-0-8176-4727-8 |
| 024 7# - OTHER STANDARD IDENTIFIER |
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| Standard number or code |
10.1007/978-0-8176-4727-8 |
| Source of number or code |
doi |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
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| Classification number |
QA313 |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
PBWR |
| Source |
bicssc |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
MAT034000 |
| Source |
bisacsh |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
515.39 |
| Edition number |
23 |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
515.48 |
| Edition number |
23 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Shafer, Douglas. |
| Relator term |
author. |
| 245 14 - TITLE STATEMENT |
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| Title |
The Center and Cyclicity Problems |
| Medium |
[electronic resource] : |
| Remainder of title |
A Computational Algebra Approach / |
| Statement of responsibility, etc. |
by Douglas Shafer, Valery Romanovski. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE |
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| Place of production, publication, distribution, manufacture |
Boston : |
| Name of producer, publisher, distributor, manufacturer |
Birkhäuser Boston, |
| Date of production, publication, distribution, manufacture, or copyright notice |
2009. |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
XII, 330 p. 4 illus. |
| Other physical details |
online resource. |
| 336 ## - CONTENT TYPE |
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| Content type term |
text |
| Content type code |
txt |
| Source |
rdacontent |
| 337 ## - MEDIA TYPE |
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| Media type term |
computer |
| Media type code |
c |
| Source |
rdamedia |
| 338 ## - CARRIER TYPE |
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| Carrier type term |
online resource |
| Carrier type code |
cr |
| Source |
rdacarrier |
| 347 ## - DIGITAL FILE CHARACTERISTICS |
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| File type |
text file |
| Encoding format |
PDF |
| Source |
rda |
| 505 0# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
Polynomial Ideals and Their Varieties -- Stability and Normal Forms -- The Center Problem -- The Isochronicity and Linearizability Problems -- Invariants of the Rotation Group -- Bifurcations of Limit Cycles and Critical Periods. |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc. |
In the last three decades, advances in methods for investigating polynomial ideals and their varieties have provided new possibilities for approaching two long-standing problems in the theory of differential equations: the Poincaré center problem and the cyclicity problem (the problem of bifurcation of limit cycles from singular trajectories). Using a computational algebra approach, this work addresses the center and cyclicity problems as behaviors of dynamical systems and families of polynomial systems. The text first lays the groundwork for computational algebra and gives the main properties of ideals in polynomial rings and their affine varieties; this is followed by a discussion regarding the theory of normal forms and stability of differential equations. The center and cyclicity problems are then explored in detail. The book contains numerous examples, pseudocode displays of all the computational algorithms, historical notes, nearly two hundred exercises, and an extensive bibliography. Completely self-contained, it is thus suitable mainly as a textbook for a graduate course in the subject but also as a reference for researchers. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Mathematics. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Algebra. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Field theory (Physics). |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Dynamics. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Ergodic theory. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Differential equations. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Partial differential equations. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Computer mathematics. |
| 650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Mathematics. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Dynamical Systems and Ergodic Theory. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Ordinary Differential Equations. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Partial Differential Equations. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Field Theory and Polynomials. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Algebra. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Computational Mathematics and Numerical Analysis. |
| 700 1# - ADDED ENTRY--PERSONAL NAME |
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| Personal name |
Romanovski, Valery. |
| Relator term |
author. |
| 710 2# - ADDED ENTRY--CORPORATE NAME |
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| Corporate name or jurisdiction name as entry element |
SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY |
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| Title |
Springer eBooks |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
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| Relationship information |
Printed edition: |
| International Standard Book Number |
9780817647261 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS |
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| Uniform Resource Identifier |
<a href="http://dx.doi.org/10.1007/978-0-8176-4727-8">http://dx.doi.org/10.1007/978-0-8176-4727-8</a> |
| 912 ## - |
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ZDB-2-SMA |