Mathematical Problems of Statistical Mechanics and Dyanamics

A Collection of Surveys

Buch | Softcover

280 Seiten

2011 | Softcover reprint of the original 1st ed. 1986
Springer (Verlag)
978-94-010-8540-3 (ISBN)

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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; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory;

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.

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. TheAsymptotics of Integrals.- 7.3. Mappings Which Possess a Smale Horseshoe.- Appendix:Ergodic Properties of Positive Matrices with Bounded Ratio of Rows.- References.- Author Index.

Reihe/Serie	Mathematics and its Applications ; 6
Reihe/Serie	Mathematics and its Applications ; 6
Zusatzinfo	280 p.
Verlagsort	Dordrecht
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Statistik
	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
	Naturwissenschaften ► Physik / Astronomie ► Thermodynamik
ISBN-10	94-010-8540-4 / 9401085404
ISBN-13	978-94-010-8540-3 / 9789401085403
Zustand	Neuware