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.
Inhaltsverzeichnis
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.
