| 000 -LEADER |
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| fixed length control field |
06027nam a2200805 i 4500 |
| 001 - CONTROL NUMBER |
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| control field |
6813366 |
| 003 - CONTROL NUMBER IDENTIFIER |
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| control field |
IEEE |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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| control field |
20200413152903.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS |
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m eo d |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION |
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cr cn |||m|||a |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
110925s2011 caua foab 001 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
|---|
| International Standard Book Number |
9781598299151 (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
|---|
| Canceled/invalid ISBN |
9781598299144 (pbk.) |
| 024 7# - OTHER STANDARD IDENTIFIER |
|---|
| Standard number or code |
10.2200/S00373ED1V01Y201107MAS011 |
| Source of number or code |
doi |
| 035 ## - SYSTEM CONTROL NUMBER |
|---|
| System control number |
(CaBNVSL)gtp00549567 |
| 035 ## - SYSTEM CONTROL NUMBER |
|---|
| System control number |
(OCoLC)752659371 |
| 040 ## - CATALOGING SOURCE |
|---|
| Original cataloging agency |
CaBNVSL |
| Transcribing agency |
CaBNVSL |
| Modifying agency |
CaBNVSL |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
|---|
| Classification number |
Q172.5.C45 |
| Item number |
C443 2011 |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
|---|
| Classification number |
500.201185 |
| Edition number |
22 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
|---|
| Personal name |
Chen, Goong, |
| Dates associated with a name |
1950- |
| 245 10 - TITLE STATEMENT |
|---|
| Title |
Chaotic maps |
| Medium |
[electronic resource] : |
| Remainder of title |
dynamics, fractals, and rapid fluctuations / |
| Statement of responsibility, etc. |
Goong Chen and Yu Huang. |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. |
|---|
| Place of publication, distribution, etc. |
San Rafael, Calif. (1537 Fourth Street, San Rafael, CA 94901 USA) : |
| Name of publisher, distributor, etc. |
Morgan & Claypool, |
| Date of publication, distribution, etc. |
c2011. |
| 300 ## - PHYSICAL DESCRIPTION |
|---|
| Extent |
1 electronic text (xiii, 227 p.) : |
| Other physical details |
ill., digital file. |
| 490 1# - SERIES STATEMENT |
|---|
| Series statement |
Synthesis lectures on mathematics and statistics, |
| International Standard Serial Number |
1938-1751 ; |
| Volume/sequential designation |
# 11 |
| 538 ## - SYSTEM DETAILS NOTE |
|---|
| System details note |
Mode of access: World Wide Web. |
| 538 ## - SYSTEM DETAILS NOTE |
|---|
| System details note |
System requirements: Adobe Acrobat Reader. |
| 500 ## - GENERAL NOTE |
|---|
| General note |
Part of: Synthesis digital library of engineering and computer science. |
| 500 ## - GENERAL NOTE |
|---|
| General note |
Series from website. |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
|---|
| Bibliography, etc. note |
Includes bibliographical references (p. 217-222) and index. |
| 505 0# - FORMATTED CONTENTS NOTE |
|---|
| Formatted contents note |
1. Simple interval maps and their iterations -- 1.1 Introduction -- 1.2 The inverse and implicit function theorems -- 1.3 Visualizing from the graphics of iterations of the quadratic map -- Notes for chapter 1 -- |
| 505 8# - FORMATTED CONTENTS NOTE |
|---|
| Formatted contents note |
2. Total variations of iterates of maps -- 2.1 The use of total variations as a measure of chaos -- Notes for chapter 2 -- |
| 505 8# - FORMATTED CONTENTS NOTE |
|---|
| Formatted contents note |
3. Ordering among periods: the Sharkovski theorem -- Notes for chapter 3 -- |
| 505 8# - FORMATTED CONTENTS NOTE |
|---|
| Formatted contents note |
4. Bifurcation theorems for maps -- 4.1 The period-doubling bifurcation theorem -- 4.2 Saddle-node bifurcations -- 4.3 The pitchfork bifurcation -- 4.4 Hopf bifurcation -- Notes for chapter 4 -- |
| 505 8# - FORMATTED CONTENTS NOTE |
|---|
| Formatted contents note |
5. Homoclinicity. Lyapunoff exponents -- 5.1 Homoclinic orbits -- 5.2 Lyapunoff exponents -- Notes for chapter 5 -- |
| 505 8# - FORMATTED CONTENTS NOTE |
|---|
| Formatted contents note |
6. Symbolic dynamics, conjugacy and shift invariant sets -- 6.1 The itinerary of an orbit -- 6.2 Properties of the shift map -- 6.3 Symbolic dynamical systems -- 6.4 The dynamics of [Sigma ...] and chaos -- 6.5 Topological conjugacy and semiconjugacy -- 6.6 Shift invariant sets -- 6.7 Construction of shift invariant sets -- 6.8 Snap-back repeller as a shift invariant set -- Notes for chapter 6 -- |
| 505 8# - FORMATTED CONTENTS NOTE |
|---|
| Formatted contents note |
7. The Smale horseshoe -- 7.1 The standard Smale horseshoe -- 7.2 The general horseshoe -- Notes for chapter 7 -- |
| 505 8# - FORMATTED CONTENTS NOTE |
|---|
| Formatted contents note |
8. Fractals -- 8.1 Examples of fractals -- 8.2 Hausdorff dimension and the Hausdorff measure -- 8.3 Iterated function systems (IFS) -- Notes for chapter 8 -- |
| 505 8# - FORMATTED CONTENTS NOTE |
|---|
| Formatted contents note |
9. Rapid fluctuations of chaotic maps on RN -- 9.1 Total variation for vector-value maps -- 9.2 Rapid fluctuations of maps on RN -- 9.3 Rapid fluctuations of systems with quasi-shift invariant sets -- 9.4 Rapid fluctuations of systems containing topological horseshoes -- 9.5 Examples of applications of rapid fluctuations -- Notes for chapter 9 -- |
| 505 8# - FORMATTED CONTENTS NOTE |
|---|
| Formatted contents note |
10. Infinite-dimensional systems induced by continuous-time difference equations -- 10.1 I3DS -- 10.2 Rates of growth of total variations of iterates -- 10.3 Properties of the set B(f ) -- 10.4 Properties of the set U(f ) -- 10.5 Properties of the set E(f ) -- Notes for chapter 10 -- |
| 505 8# - FORMATTED CONTENTS NOTE |
|---|
| Formatted contents note |
A. Introduction to continuous-time dynamical systems -- The local behavior of 2-dimensional nonlinear systems -- Index for two-dimensional systems -- The Poincare map for a periodic orbit in RN -- B. Chaotic vibration of the wave equation due to energy pumping and van der Pol boundary conditions -- The mathematical model and motivations -- Chaotic vibration of the wave equation -- Authors' biographies -- Index. |
| 506 1# - RESTRICTIONS ON ACCESS NOTE |
|---|
| Terms governing access |
Abstract freely available; full-text restricted to subscribers or individual document purchasers. |
| 510 0# - CITATION/REFERENCES NOTE |
|---|
| Name of source |
Compendex |
| 510 0# - CITATION/REFERENCES NOTE |
|---|
| Name of source |
INSPEC |
| 510 0# - CITATION/REFERENCES NOTE |
|---|
| Name of source |
Google scholar |
| 510 0# - CITATION/REFERENCES NOTE |
|---|
| Name of source |
Google book search |
| 520 3# - SUMMARY, ETC. |
|---|
| Summary, etc. |
This book consists of lecture notes for a semester-long introductory graduate course on dynamical systems and chaos taught by the authors at Texas A&M University and Zhongshan University, China. There are ten chapters in the main body of the book, covering an elementary theory of chaotic maps in finite-dimensional spaces. The topics include one-dimensional dynamical systems (interval maps), bifurcations, general topological, symbolic dynamical systems, fractals and a class of infinite-dimensional dynamical systems which are induced by interval maps, plus rapid fluctuations of chaotic maps as a new viewpoint developed by the authors in recent years.Two appendices are also provided in order to ease the transitions for the readership from discrete-time dynamical systems to continuous-time dynamical systems, governed by ordinary and partial differential equations. |
| 530 ## - ADDITIONAL PHYSICAL FORM AVAILABLE NOTE |
|---|
| Additional physical form available note |
Also available in print. |
| 588 ## - SOURCE OF DESCRIPTION NOTE |
|---|
| Source of description note |
Title from PDF t.p. (viewed on September 25, 2011). |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Chaotic behavior in systems |
| General subdivision |
Mathematics. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Mappings (Mathematics) |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
chaos |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
interval maps |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
periodicity |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
sensitive dependence |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
stability |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
Sharkovski's theorem |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
bifurcations |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
homoclinicity |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
symbolic dynamics |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
smale horseshoe |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
total variations |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
rapid fluctuations |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
fractals |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
wave equation |
| 700 1# - ADDED ENTRY--PERSONAL NAME |
|---|
| Personal name |
Huang, Yu, |
| Dates associated with a name |
1963- |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
|---|
| Relationship information |
Print version: |
| International Standard Book Number |
9781598299144 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE |
|---|
| Uniform title |
Synthesis digital library of engineering and computer science. |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE |
|---|
| Uniform title |
Synthesis lectures on mathematics and statistics, |
| International Standard Serial Number |
1938-1751 ; |
| Volume/sequential designation |
# 11. |
| 856 42 - ELECTRONIC LOCATION AND ACCESS |
|---|
| Materials specified |
Abstract with links to resource |
| Uniform Resource Identifier |
http://ieeexplore.ieee.org/servlet/opac?bknumber=6813366 |
