Ultra Poincar�e chaos and alpha labeling : (Record no. 68468)
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| fixed length control field | 07000nam a2200721 i 4500 |
| 001 - CONTROL NUMBER | |
| control field | 9780750351621 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | IOP |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20251030124828.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS | |
| fixed length control field | m eo d |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr cn |||m|||a |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 241213s2024 enka fob 000 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9780750351621 |
| Qualifying information | ebook |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9780750351614 |
| Qualifying information | mobi |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9780750351607 |
| Qualifying information | |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9780750351638 |
| Qualifying information | myPrint |
| 024 7# - OTHER STANDARD IDENTIFIER | |
| Standard number or code | 10.1088/978-0-7503-5162-1 |
| Source of number or code | doi |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (CaBNVSL)thg00084069 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)1475037933 |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | CaBNVSL |
| Language of cataloging | eng |
| Description conventions | rda |
| Transcribing agency | CaBNVSL |
| Modifying agency | CaBNVSL |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | Q172.5.C45 |
| Item number | A458 2024eb |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | PBWS |
| Source | bicssc |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | MAT007000 |
| Source | bisacsh |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Akhmet, Marat, |
| Relator term | author. |
| 9 (RLIN) | 96937 |
| 245 1# - TITLE STATEMENT | |
| Title | Ultra Poincar�e chaos and alpha labeling : |
| Remainder of title | a new approach to chaotic dynamics / |
| Statement of responsibility, etc. | Marat Akhmet. |
| 246 3# - VARYING FORM OF TITLE | |
| Title proper/short title | New approach to chaotic dynamics. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : |
| Name of producer, publisher, distributor, manufacturer | IOP Publishing, |
| Date of production, publication, distribution, manufacture, or copyright notice | [2024] |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (various pagings) : |
| Other physical details | illustrations (some color). |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | electronic |
| Source | isbdmedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Source | rdacarrier |
| 490 1# - SERIES STATEMENT | |
| Series statement | [IOP release $release] |
| 490 1# - SERIES STATEMENT | |
| Series statement | IOP ebooks. [2024 collection] |
| 500 ## - GENERAL NOTE | |
| General note | "Version: 20241101"--Title page verso. |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE | |
| Bibliography, etc | Includes bibliographical references. |
| 505 ## - FORMATTED CONTENTS NOTE | |
| Formatted contents note | part I. Introduction. 1. Historical and philosophical overview -- 1.1. Outline -- 1.2. A new mathematical structure -- 1.3. Alpha labels in spiraled hierarchy of mathematical structures -- 1.4. Universality and minimalism of alpha labeling and unpredictability -- 1.5. Principle of excessiveness : the Universe approximates science -- 1.6. Potential and actual uncertainty in dynamics -- 1.7. Actual uncertainty of chaos -- 1.8. Monads spiral up to abstract similarity -- 1.9. Alpha labeling for more chaos and fractals -- 1.10. Ancient Greek chaos -- 1.11. Alpha unpredictability and alpha labeling decrease formalism of chaos -- 1.12. Mathematical chaos and H. Poincar�e -- 1.13. Alpha unpredictability versus sensitivity -- 1.14. Ultra Poincar�e chaos versus Li-Yorke chaos -- 1.15. Chaos as a metaphor -- 1.16. Does the theory of chaos exist? -- 1.17. Ubiquitous chaos and dualism -- 1.18. Domain of chaos |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | part II. Alpha labeling and unpredictability. 2. Alpha labels are a new mathematical structure -- 2.1. Sets of alpha labels and alpha map -- 2.2. Alpha dynamics -- 2.3. Alpha chaos -- 2.4. Examples of alpha chaotic models -- 2.5. Hyperbolic alpha labeling -- 2.6. Modular chaos -- 2.7. Abstract fractals : alpha spaces with measures -- 2.8. Notes |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 3. Alpha unpredictability implies a universal mathematical chaos -- 3.1. Poincar�e and Lorenz lines in a nutshell -- 3.2. An individual chaos : alpha unpredictability -- 3.3. Alpha unpredictable functions : appearance of chaos -- 3.4. Notes |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | part III. Compartmental functions. 4. Compartmental alpha unpredictable functions -- 4.1. Continuous compartmental unpredictable functions -- 4.2. Discontinuous compartmental periodic Poisson stable functions -- 4.3. Algebra and significance for applications -- 4.4. Notes |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | part IV. Differential equations with ultra Poincar�e chaos. 5. Alpha unpredictable differential equations -- 5.1. Strongly alpha unpredictable solutions -- 5.2. Compartmental quasi-linear equations -- 5.3. Modulo periodic Poisson stable solutions -- part V. Numerical alpha unpredictability. 6. Ultra Poincar�e chaos numerically -- 6.1. Introduction and preliminaries -- 6.2. The algorithm of the test and the application procedure -- 6.3. Ultra Poincar�e chaos for revisited models -- 6.4. Alpha unpredictability test is positive for known strange non-chaotic attractors -- 6.5. The generalized synchronization as a proof of alpha unpredictability -- 6.6. Notes |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | part VI. Randomness and alpha labeling. 7. Alpha labeled randomness -- 7.1. Alpha unpredictability in Bernoulli schemes -- 7.2. Alpha unpredictable functions randomly -- 7.3. Alpha unpredictable strings and statistical laws -- 7.4. Modular chaos in random processes |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | part VII. Markov chains and differential equations. 8. Markov chains and stochastic differential equations -- 8.1. Alpha chaos in Markov chains -- 8.2. Duffing type equations with Markov coefficients -- 8.3. Notes |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | part VIII. Fractals with alpha spaces. 9. Alpha induced dynamics in fractals and cubes -- 9.1. Historical observations -- 9.2. Alpha induced dynamics in metric spaces -- 9.3. Chaotic cubes -- 9.4. Alpha chaos in Fatou-Julia iterations -- 9.5. Notes. |
| 506 ## - RESTRICTIONS ON ACCESS NOTE | |
| Terms governing access | Full-text restricted to subscribers or individual document purchasers. |
| 520 3# - SUMMARY, ETC. | |
| Summary, etc. | This book serves as a comprehensive and detailed collection of knowledge on two innovative aspects of our research: ultra Poincar�e chaos and alpha labeling. The first concept represents a fundamental trait of dynamical complexity, while the second acts as an algorithmic tool to analyse and construct complexity within the dynamics, probabilities, and geometries of science and industry. The manuscript aims to provide solid guidance for studying complexities through rigorous mathematical methods. The chaos is derived from the dynamical characteristic of alpha unpredictability, representing a modernized version of Poisson stability motion. It builds upon the foundational work of Poincar�e and Birkhoff, incorporating key new insights that expand upon the French genius's contributions to the recurrence theorem, applicable in contexts such as the three-body problem. |
| 521 ## - TARGET AUDIENCE NOTE | |
| Target audience note | Those researching or studying dynamical systems, chaos, differential equations, and stochastic differential equations. |
| 530 ## - ADDITIONAL PHYSICAL FORM AVAILABLE NOTE | |
| Additional physical form available note | Also available in print. |
| 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, EPUB reader, or Kindle reader. |
| 545 ## - BIOGRAPHICAL OR HISTORICAL DATA | |
| Biographical or historical data | Dr. Marat Akhmet is presently a Professor in the Department of Mathematics at METU in Ankara, Turkey. In recent years, he has been exploring continuous and discontinuous dynamics, artificial neural networks alongside stability, chaos, and fractals. He has authored eight books and published over two hundred scientific papers. |
| 588 ## - SOURCE OF DESCRIPTION NOTE | |
| Source of description note | Title from PDF title page (viewed on December 13, 2024). |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | |
| 9 (RLIN) | 96938 |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | |
| 9 (RLIN) | 65524 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | |
| Source of heading or term | bicssc |
| 9 (RLIN) | 96939 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | |
| Source of heading or term | bisacsh |
| 9 (RLIN) | 96940 |
| 710 2# - ADDED ENTRY--CORPORATE NAME | |
| Corporate name or jurisdiction name as entry element | Institute of Physics (Great Britain), |
| Relator term | publisher. |
| 9 (RLIN) | 17702 |
| 776 #8 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| International Standard Book Number | 9780750351607 |
| -- | 9780750351638 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | IOP (Series). |
| Name of part/section of a work | Release 24. |
| 9 (RLIN) | 96941 |
| 830 ## - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | IOP ebooks. |
| Name of part/section of a work | 2024 collection. |
| 9 (RLIN) | 96942 |
| 856 4# - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://iopscience.iop.org/book/mono/978-0-7503-5162-1">https://iopscience.iop.org/book/mono/978-0-7503-5162-1</a> |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
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