P-Adic Deterministic and Random Dynamics

2004. Auflage 2004
ISBN: 978-1-4020-2659-1
Verlag: Springer

Buch, Englisch, Band 574, 270 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1290 g

Reihe: Mathematics and Its Applications

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.

Zielgruppe

Research

Autoren/Hrsg.

Khrennikov, Andrei Y

Nilsson, Marcus

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Sozialwissenschaften Psychologie Allgemeine Psychologie Kognitionspsychologie
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Naturwissenschaften Physik Mechanik
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik

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.