Mathematical Problems of Statistical Mechanics and Dyanamics A Collection of Surveys

Mathematical Problems of Statistical Mechanics and Dyanamics A Collection of Surveys / edited by R.L. Dobrushin.

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'....

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Bibliographic Details
Corporate Author: SpringerLink (Online service)
Other Authors: Dobrushin, R.L (Editor)
Format: eBook
Language:English
Published: Dordrecht : Springer Netherlands : Imprint: Springer, 1986.
Edition:1st ed. 1986.
Series:Mathematics and its Applications, Soviet Series, 6
Springer eBook Collection.
Subjects:
Statistical physics.
Dynamical systems.
Applied mathematics.
Engineering mathematics.
Statistics .
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • 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.

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