Applied algebraic dynamics
By: by Vladimir Anashin and Andrei Khrennikov
Contributors: Khrennikov, A. I͡U. (Andreĭ I͡Urʹevich), 1958-
Series: De Gruyter expositions in mathematics -- 49
Publisher: Walter De Gruyter
Published: 2009
Place of publication: Berlin; New York
Language: eng
Number of pages: 533
ISBN-13: 9783110203004
Subjects: Arithmetical algebraic geometry; Differentiable dynamical systems
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. For students and researchers working on the theory of dynamical systems, algebra, number theory, measure theory, computer sciences, cryptography, and image analysis.
Table of contents: title: Algebraic and number-theoretic background; title: The commutative non-Archimedean dynamics; title: Dynamics on algebraic structures; title: p-adic analysis; title: p-adic ergodic theory; title: Asymptotic distribution of cycles; title: The non-commutative non-Archimedean dynamics; title: Basics of polynomial dynamics on groups; title: Ergodic polynomials over groups with operators; title: Applications; title: Automata, computers, combinatorics; title: Pseudorandom numbers; title: Stream ciphers; title: Structure of trajectories; title: p-adic probability theory; title: p-adic valued quantization; title: m-adic modeling in cognitive science and psychology; title: Neuronal hierarchy behind the ultrametric mental space; title: Gene expression from dynamics in the 2-adic space; title: Genetic code on the diadic plane.