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001 9780750351621
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020 _a9780750351621
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024 7 _a10.1088/978-0-7503-5162-1
_2doi
035 _a(CaBNVSL)thg00084069
035 _a(OCoLC)1475037933
040 _aCaBNVSL
_beng
_erda
_cCaBNVSL
_dCaBNVSL
050 4 _aQ172.5.C45
_bA458 2024eb
072 7 _aPBWS
_2bicssc
072 7 _aMAT007000
_2bisacsh
100 1 _aAkhmet, Marat,
_eauthor.
_996937
245 1 _aUltra Poincar�e chaos and alpha labeling :
_ba new approach to chaotic dynamics /
_cMarat Akhmet.
246 3 _aNew approach to chaotic dynamics.
264 1 _aBristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) :
_bIOP Publishing,
_c[2024]
300 _a1 online resource (various pagings) :
_billustrations (some color).
336 _atext
_2rdacontent
337 _aelectronic
_2isbdmedia
338 _aonline resource
_2rdacarrier
490 1 _a[IOP release $release]
490 1 _aIOP ebooks. [2024 collection]
500 _a"Version: 20241101"--Title page verso.
504 _aIncludes bibliographical references.
505 _apart 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 _apart 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 _a3. 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 _apart 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 _apart 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 _apart 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 _apart 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 _apart 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 _aFull-text restricted to subscribers or individual document purchasers.
520 3 _aThis 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 _aThose researching or studying dynamical systems, chaos, differential equations, and stochastic differential equations.
530 _aAlso available in print.
538 _aMode of access: World Wide Web.
538 _aSystem requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.
545 _aDr. 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 _aTitle from PDF title page (viewed on December 13, 2024).
650 _aChaotic behavior in systems.
_996938
650 _aDynamics.
_965524
650 7 _aChaos theory.
_2bicssc
_996939
650 7 _aMATHEMATICS / Differential Equations / General.
_2bisacsh
_996940
710 2 _aInstitute of Physics (Great Britain),
_epublisher.
_917702
776 8 _iPrint version:
_z9780750351607
_z9780750351638
830 0 _aIOP (Series).
_pRelease 24.
_996941
830 _aIOP ebooks.
_p2024 collection.
_996942
856 4 _uhttps://iopscience.iop.org/book/mono/978-0-7503-5162-1
942 _cE-Books
999 _c68468
_d68468