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.

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"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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