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Author: Andrei Y. Khrennikov Publisher: Springer Science & Business Media ISBN: 1402026609 Category : Science Languages : en Pages : 279
Book Description
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.
Author: Andrei Y. Khrennikov Publisher: Springer Science & Business Media ISBN: 1402026609 Category : Science Languages : en Pages : 279
Book Description
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.
Author: Andrzej Lasota Publisher: Cambridge University Press ISBN: 9780521090964 Category : Mathematics Languages : en Pages : 376
Book Description
This book shows how densities arise in simple deterministic systems. There has been explosive growth in interest in physical, biological and economic systems that can be profitably studied using densities. Due to the inaccessibility of the mathematical literature there has been little diffusion of the applicable mathematics into the study of these 'chaotic' systems. This book will help to bridge that gap. The authors give a unified treatment of a variety of mathematical systems generating densities, ranging from one-dimensional discrete time transformations through continuous time systems described by integro-partial differential equations. They have drawn examples from many scientific fields to illustrate the utility of the techniques presented. The book assumes a knowledge of advanced calculus and differential equations, but basic concepts from measure theory, ergodic theory, the geometry of manifolds, partial differential equations, probability theory and Markov processes, and stochastic integrals and differential equations are introduced as needed.
Author: Ludwig Arnold Publisher: Springer Science & Business Media ISBN: 3662128780 Category : Mathematics Languages : en Pages : 590
Book Description
The first systematic presentation of the theory of dynamical systems under the influence of randomness, this book includes products of random mappings as well as random and stochastic differential equations. The basic multiplicative ergodic theorem is presented, providing a random substitute for linear algebra. On its basis, many applications are detailed. Numerous instructive examples are treated analytically or numerically.
Author: Yu V Egorov Publisher: World Scientific ISBN: 9814476005 Category : Mathematics Languages : en Pages : 393
Book Description
The mutual influence between mathematics and science and technology is becoming more and more widespread with profound connections among them being discovered. In particular, important connections between harmonic analysis, wavelet analysis and p-adic analysis have been found recently.This volume reports these findings and guides the reader towards the latest areas for further research. It is divided into two parts: harmonic, wavelet and p-adic analysis and p-adic and stochastic analysis.
Author: Rabindra Nath Bhattacharya Publisher: ISBN: 9780511274367 Category : Random dynamical systems Languages : en Pages : 463
Book Description
This treatment provides an exposition of discrete time dynamic processes evolving over an infinite horizon. Chapter 1 reviews some mathematical results from the theory of deterministic dynamical systems, with particular emphasis on applications to economics. The theory of irreducible Markov processes, especially Markov chains, is surveyed in Chapter 2. Equilibrium and long run stability of a dynamical system in which the law of motion is subject to random perturbations is the central theme of Chapters 3-5. A unified account of relatively recent results, exploiting splitting and contractions, that have found applications in many contexts is presented in detail. Chapter 6 explains how a random dynamical system may emerge from a class of dynamic programming problems. with examples and exercises, readers are guided from basic theory to the frontier of applied mathematical research.
Author: M. Berz Publisher: American Mathematical Soc. ISBN: 0821847406 Category : Mathematics Languages : en Pages : 281
Book Description
This volume contains the proceedings of the Tenth International Conference on $p$-adic and Non-Archimedean Analysis, held at Michigan State University in East Lansing, Michigan, on June 30-July 3, 2008. This volume contains a kaleidoscope of papers based on several of the more important talks presented at the meeting. It provides a cutting-edge connection to some of the most important recent developments in the field. Through a combination of survey papers, research articles, and extensive references to earlier work, this volume allows the reader to quickly gain an overview of current activity in the field and become acquainted with many of the recent sub-branches of its development.
Author: Andrei Y. Khrennikov
Author: Andrei Y. Khrennikov
Author: Andrei Y Khrennikov
Author: Andrzej Lasota
Author: Ludwig Arnold
Author: 
Author: G. B. Folland
Author: Yu V Egorov
Author: Rabindra Nath Bhattacharya
Author: M. Berz
Author: S. Albeverio