Applied Algebraic Dynamics

1. Auflage 2009
ISBN: 978-3-11-020300-4
Verlag: De Gruyter

Buch, Englisch, Band 49, 533 Seiten, HC runder Rücken kaschiert, Format (B × H): 175 mm x 246 mm, Gewicht: 1117 g

Reihe: De Gruyter Expositions in Mathematics

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.

Zielgruppe

Researchers, Graduate Students of Mathematics; University Libraries

Autoren/Hrsg.

Khrennikov, Andrei

Anashin, Vladimir

Fachgebiete

• Mathematik | Informatik EDV | Informatik Technische Informatik Computersicherheit Kryptographie, Datenverschlüsselung
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Algebra Zahlentheorie

Inhaltsverzeichnis

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

Über Autor(innen)

Vladimir Anashin, Russian State University, Moscow, Russia; Andrei Khrennikov, Växjö University, Sweden.