Applied Algebraic Dynamics
1st Edition
Published on 17. June 2009
Book
Hardback
XXIV, 533 pages
978-3-11-020300-4 (ISBN)
Description
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.
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For students and researchers working on the theory of dynamical systems, algebra, number theory, measure theory, computer sciences, cryptography, and image analysis.
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Vladimir Anashin | Andrei Khrennikov
Applied Algebraic Dynamics
Book
06/2009
1st Edition
De Gruyter
€229.00
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Vladimir Anashin | Andrei Khrennikov
Applied Algebraic Dynamics
E-Book
06/2009
1st Edition
De Gruyter
€210.00
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Persons
Vladimir Anashin, Russian State University, Moscow, Russia; Andrei Khrennikov, Växjö University, Sweden.
Content
Frontmatter
Contents
Chapter 1. Algebraic and number-theoretic background
I. The Commutative Non-Archimedean Dynamics
Chapter 2. Dynamics on algebraic structures
Chapter 3. p-adic analysis
Chapter 4. p-adic ergodic theory
Chapter 5. Asymptotic distribution of cycles
II. The Non-Commutative Non-Archimedean Dynamics
Chapter 6. Basics of polynomial dynamics on groups
Chapter 7. Ergodic polynomials over groups with operators
III. Applications
Chapter 8. Automata, computers, combinatorics
Chapter 9. Pseudorandom numbers
Chapter 10. Stream ciphers
Chapter 11. Structure of trajectories
Chapter 12. p-adic probability theory
Chapter 13. p-adic valued quantization
Chapter 14. m-adic modeling in cognitive science and psychology
Chapter 15. Neuronal hierarchy behind the ultrametric mental space
Chapter 16. Gene expression from dynamics in the 2-adic space
Chapter 17. Genetic code on the diadic plane
Backmatter
Contents
Chapter 1. Algebraic and number-theoretic background
I. The Commutative Non-Archimedean Dynamics
Chapter 2. Dynamics on algebraic structures
Chapter 3. p-adic analysis
Chapter 4. p-adic ergodic theory
Chapter 5. Asymptotic distribution of cycles
II. The Non-Commutative Non-Archimedean Dynamics
Chapter 6. Basics of polynomial dynamics on groups
Chapter 7. Ergodic polynomials over groups with operators
III. Applications
Chapter 8. Automata, computers, combinatorics
Chapter 9. Pseudorandom numbers
Chapter 10. Stream ciphers
Chapter 11. Structure of trajectories
Chapter 12. p-adic probability theory
Chapter 13. p-adic valued quantization
Chapter 14. m-adic modeling in cognitive science and psychology
Chapter 15. Neuronal hierarchy behind the ultrametric mental space
Chapter 16. Gene expression from dynamics in the 2-adic space
Chapter 17. Genetic code on the diadic plane
Backmatter