P-adic Deterministic and Random Dynamics [Hardcover]

This book provides an overview of the theory of p-adic (and more general non-Archimedean) dynamical systems. The main part of the book is devoted to discrete dynamical systems. It presents a model of probabilistic thinking on p-adic mental space based on ultrametric diffusion. Coverage also details p-adic neural networks and their applications to cognitive sciences: learning algorithms, memory recalling.

1. On Applications of P-Adic Analysis.- 2. P-Adic Numbers and P-Adic Analysis.- 3. P-Adic Dynamical Systems.- 4. Perturbation of Monomial Systems.- 5. Dynamical Systems in Finite Extensions of ?P.- 6. Conjugate Maps.- 7. P-Adic Ergodicity.- 8. P-Adic Neural Networks.- 9. Dynamics in Ultra-Pseudometric Spaces.- 10. Random Dynamics.- 11. Dynamics of Probability Distributions on the P-Adic Mental Space.- 12. Ultrametric Wavelets and Their Applications.- 13. Theory of P-Adic Valued Probability.- References.

From the reviews:

The growing interest in non-Archimedean counterparts of virtually all main notions of classical mathematics and could not leave out holomorphic dynamics, one of the central subjects of modern analysis. & The authors of this book are among the most active contributors & and their results constitute the main material of the book. & The book will be interesting both to specialists in dynamical systems wishing to see the p-adic face of their field, and to readers looking for new applications of mathematics & . (Anatoly N. Kochubei, Mathematical Reviews, 2005h)

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