最 低 价：￥838.80
定 价：￥932.00
作 者：Andrei Yu. Khrennikov，MarcusNilsson 著 著
出 版 社：化学工业出版社
出版时间：2004-12-1
I S B N：9781402026591
| Dedication Foreword Acknowledgments 1. ON APPLICATIONS OF P-ADIC ANALYSIS 2. P-AD1C NUMBERS AND P-ADIC ANALYSIS 1 Ultrametric spaces 2 Non-archimedean fields 3 The field of p-adic numbers 4 Tree-like structure of the p-adic numbers 5 Extensions of the field of p-adic numbers 6 Analysis in complete non-Archimedean fields 7 Analytic functions 8 Hensel's lemma 9 Roots of unity 10 Some facts from number theory 3. P-ADIC DYNAMICAL SYSTEMS 1 Periodic points and their character 2 Monomial dynamical systems 4. PERTURBATION OF MONOMIAL SYSTEMS 1 Existence of Fixed Points of a Perturbated System 2 CycLes of Perturbed Systems 5. DYNAMICAL SYSTEMS IN FINITE EXTENSIONS OF Qp 1 Some examples on behaviour of polynomial dynamical systems in finite extensions. 2 Polynomial dynamical systems over local fields 6. CONJUGATE MAPS 1 Introduction 2 Attracting fixed points 3 Repelling fixed points 4 Small denominators 5 Neutrally stable fixed points in Cv 7. P-ADIC ERGODICITY 1 Minimality. 2 Unique ergodicity. 8. P-ADIC NEURAL NETWORKS 1 Hierarchical synaptic potentials 2 Multidimensional case 3 inimization algorithm of learning 4 Parametric dynamical networks 5 p-adic model for memory retrieval 9. DYNAMICS IN ULTRA-PSEUDOMETRIC SPACES 1 Extension of the p-adic mental model: associations and ideas 2 Dynamics in pseudometric spaces of sets 3 Existence of attractors 4 Thinking with constant sharpness of associations 5 Thinking with increasing sharpness of associations 6 Strong triangle inequality for Hausdorff's pseudometric 10. RANDOM DYNAMICS 1 Introduction to the theory of random dynamical systems 2 Random dynamics for monomial maps 3 Definition of Markovian dynamics 4 Conditions for Markovian dynamics 5 Concluding remarks …… 11. DYNAMICS OF PROBABILITYDISTRIBUTIONS ON THE 12. ULTRAMETRIC WAVELETS AND THEIR APPLICATIONS References Index |
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