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Field name	Details
Dewey Class	621
Title	Mathematical Problems of Statistical Mechanics and Dyanamics ([EBook] :) : A Collection of Surveys / / edited by R. L. Dobrushin.
Added Personal Name	Dobrushin, R. L. editor.
Other name(s)	SpringerLink (Online service)
Publication	Dordrecht : : Springer Netherlands, , 1986.
Physical Details	280 p. : online resource.
Series	Mathematics and its applications. Soviet series 0169-6378 ; ; 6
ISBN	9789400945920
Summary Note	Approach your problems from the It isn't that they can't see the solution. right end and begin with the answers. It is that they can't see the problem. Then one day, perhaps you will find the final question. G. K. Chesterton. The Scandal of Father Brown 'The point of a Pin'. 'The Hermit Clad in Crane Feathers' in R. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the 'tree' of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as 'experimental mathematics', 'CFD', 'completely integrable systems', 'chaos, synergetics and large-scale order', which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.:
Contents note	Phase Diagrams for Continuous-Spin Models: An Extension of the Pirogov-Sinai Theory -- 1. Formulation of the Main Result -- 2. Preliminaries -- 3. The Main Lemma -- 4. Proof of the Main Lemma -- References -- Space-Time Entropy of Infinite Classical Systems -- 1. Introduction -- 2. Statistical Estimates of the Gibbs Distribution -- 3. Reduction to Partial Flows -- 4. Estimate of Space-Time Entropy -- References -- Spectrum Analysis and Scattering Theory for a Three-Particle Cluster Operator -- 1. Introduction. A General Definition of the Cluster Operator -- 2. Three-Particle Cluster Operators -- 3. Equations for the Resolvent of a Self-Adjoint Three-Particle Cluster Operator -- 4. Study of Equations (3.4)–(3.6) -- 5. The Main Result -- 6. Proof of Theorem 5.11 (Scattering Theory) -- References -- Stochastic Attractors and their Small Perturbations -- 1. Introduction -- 2. Dynamical Systems with Stochastic Attractors -- 3. Stochastic Perturbations (Regular Case) -- 4. The Law of Exponential Decay and Small Stochastic Perturbations -- 5. Stochastic Perturbations (Singular Case) -- 6. Small Quasi-Stochastic Perturbations -- 7. Ergodic Properties of Dynamical System Discretizations -- References -- Statistical Properties of Smooth Smale Horseshoes -- 1. General Background -- 2. Expanding and Contracting Fibrations of a Smale Horseshoe -- 3. Smooth Invariant Conditional Probability Distributions on Fibrations -- 4. Smooth Non-Singular Probability Distributions on a Smale Horseshoe -- 5. A Natural Invariant Probability Distribution on the Hyperbolic Set of a Smale Horseshoe -- 6. Some Properties of the Constructed Limit Probability Distributions on a Smale Horseshoe -- 7. Evolution of Probability Distributions on a Smale Horseshoe -- 7.1. Asymptotic Inequalities for Measures and Integrals -- 7.2. The Asymptotics of Integrals -- 7.3. Mappings Which Possess a Smale Horseshoe -- Appendix:Ergodic Properties of Positive Matrices with Bounded Ratio of Rows -- References -- Author Index.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-94-009-4592-0
Links to Related Works	Subject References: Applications of Mathematics . Applied mathematics . Dynamical Systems . Engineering mathematics . Physics . Statistical Physics . Statistical Physics, Dynamical Systems and Complexity . Statistics . Statistics, general . Authors: Dobrushin, R. L. . Corporate Authors: SpringerLink (Online service) . Series: Mathematics and its applications. Soviet series . Classification: 621 .

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Mathematical Problems of Statistical Mechanics and Dyanamics: A Collection of Surveys /

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