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Applied Algebraic Dynamics
-
Vladimir Anashin
Language:
English
Published/Copyright:
2009
About this book
This monograph presents recent developments of the theory of algebraic dynamical systems and their applications to computer sciences, cryptography, cognitive sciences, psychology, image analysis, and numerical simulations. The most important mathematical results presented in this book are in the fields of ergodicity, p-adic numbers, and noncommutative groups.
- For students and researchers working on the theory of dynamical systems, algebra, number theory, measure theory, computer sciences, cryptography, and image analysis.
Author / Editor information
Vladimir Anashin, Russian State University, Moscow, Russia; Andrei Khrennikov, Växjö University, Sweden.
Topics
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Frontmatter
i -
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Contents
xix -
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Chapter 1. Algebraic and number-theoretic background
1 - I. The Commutative Non-Archimedean Dynamics
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Chapter 2. Dynamics on algebraic structures
37 -
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Chapter 3. p-adic analysis
48 -
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Chapter 4. p-adic ergodic theory
90 -
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Chapter 5. Asymptotic distribution of cycles
162 - II. The Non-Commutative Non-Archimedean Dynamics
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Chapter 6. Basics of polynomial dynamics on groups
199 -
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Chapter 7. Ergodic polynomials over groups with operators
205 - III. Applications
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Chapter 8. Automata, computers, combinatorics
245 -
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Chapter 9. Pseudorandom numbers
269 -
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Chapter 10. Stream ciphers
305 -
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Chapter 11. Structure of trajectories
340 -
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Chapter 12. p-adic probability theory
377 -
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Chapter 13. p-adic valued quantization
415 -
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Chapter 14. m-adic modeling in cognitive science and psychology
433 -
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Chapter 15. Neuronal hierarchy behind the ultrametric mental space
468 -
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Chapter 16. Gene expression from dynamics in the 2-adic space
487 -
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Chapter 17. Genetic code on the diadic plane
494 -
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Backmatter
503
Publishing information
Pages and Images/Illustrations in book
eBook published on:
June 2, 2009
eBook ISBN:
9783110203011
Hardcover published on:
June 17, 2009
Hardcover ISBN:
9783110203004
Pages and Images/Illustrations in book
Front matter:
24
Main content:
533
Keywords for this book
Algebraic Dynamical Systems; p-adic Numbers; Measure-Preserving Transformations; Ergodicity; Profinite Groups; Automata; Computer Sciences; Cryptography; p-adic Probability; Quantum Theory; Psychology; Genetics; Latin Squares; Pseudorandom Generators; Stream Ciphers.
Audience(s) for this book
Researchers, Graduate Students of Mathematics; University Libraries
Safety & product resources
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Manufacturer information:
Walter de Gruyter GmbH
Genthiner Straße 13
10785 Berlin
productsafety@degruyterbrill.com
