Dynamical systems, ergodic theory and applications (2000)

Public ISBD Titre : Dynamical systems, ergodic theory and applications Type de document : texte imprimé Auteurs : Iakov Grigorievitch Sinaï, Éditeur scientifique Mention d'édition : 2 éd Editeur : Berlin ; London ; Cham : Springer Année de publication : 2000 Collection : Encyclopaedia of mathematical sciences Sous-collection : Mathematical physics num. Vol 100 Importance : X-459 p. Présentation : ill. Format : 24 cm ISBN/ISSN/EAN : 978-3-540-66316-4 Note générale : Bibliogr. Langues : Anglais (eng) Mots-clés : Théorie ergodique Systèmes dynamiques Index. décimale : 536.75 Entropie. Thermodynamique statistique. Processus irréversibles. Résumé : This EMS volume, the first edition of which was published as Dynamical Systems II, EMS 2, sets out to familiarize the reader to the fundamental ideas and results of modern ergodic theory and its applications to dynamical systems and statistical mechanics. The exposition starts from the basic of the subject, introducing ergodicity, mixing and entropy. The ergodic theory of smooth dynamical systems is treated. Numerous examples are presented carefully along with the ideas underlying the most important results. Moreover, the book deals with the dynamical systems of statistical mechanics, and with various kinetic equations. For this second enlarged and revised edition, published as Mathematical Physics I, EMS 100, two new contributions on ergodic theory of flows on homogeneous manifolds and on methods of algebraic geometry in the theory of interval exchange transformations were added. This book is compulsory reading for all mathematicians working in this field, or wanting to learn about it. Note de contenu : I. General ergodic theory of groups of measure preserving transformations - Basic notions of Ergodic theory and examples of dynamical systems - Spectral theory of dynamical systems - Entropy theory of dynamical systems - Periodic approximations and their applications. Ergodic theorems, spectral and entropy theory for the general group actions - Trajectory theory II. Ergodic theory of smooth dynamical systems - Stochasticity of smooth dynamical systems. The elements of KAM-theory - General theory of smooth hyperbolic dynamical systems - Billiards and other hyperbolic systems - Ergodic theory of one-dimensional mappings III. Dynamical systems on homogeneous spaces - Dynamical systems on homogeneous spaces IV. The dynamics of billiards flows in rational polygons Dynamical systems, ergodic theory and applications [texte imprimé] / Iakov Grigorievitch Sinaï, Éditeur scientifique  . -  2 éd . - Berlin ; London ; Cham : Springer, 2000 . - X-459 p. : ill. ; 24 cm. - (Encyclopaedia of mathematical sciences. Mathematical physics; Vol 100) . ISBN : 978-3-540-66316-4 Bibliogr. Langues : Anglais (eng) Mots-clés : Théorie ergodique Systèmes dynamiques Index. décimale : 536.75 Entropie. Thermodynamique statistique. Processus irréversibles. Résumé : This EMS volume, the first edition of which was published as Dynamical Systems II, EMS 2, sets out to familiarize the reader to the fundamental ideas and results of modern ergodic theory and its applications to dynamical systems and statistical mechanics. The exposition starts from the basic of the subject, introducing ergodicity, mixing and entropy. The ergodic theory of smooth dynamical systems is treated. Numerous examples are presented carefully along with the ideas underlying the most important results. Moreover, the book deals with the dynamical systems of statistical mechanics, and with various kinetic equations. For this second enlarged and revised edition, published as Mathematical Physics I, EMS 100, two new contributions on ergodic theory of flows on homogeneous manifolds and on methods of algebraic geometry in the theory of interval exchange transformations were added. This book is compulsory reading for all mathematicians working in this field, or wanting to learn about it. Note de contenu : I. General ergodic theory of groups of measure preserving transformations - Basic notions of Ergodic theory and examples of dynamical systems - Spectral theory of dynamical systems - Entropy theory of dynamical systems - Periodic approximations and their applications. Ergodic theorems, spectral and entropy theory for the general group actions - Trajectory theory II. Ergodic theory of smooth dynamical systems - Stochasticity of smooth dynamical systems. The elements of KAM-theory - General theory of smooth hyperbolic dynamical systems - Billiards and other hyperbolic systems - Ergodic theory of one-dimensional mappings III. Dynamical systems on homogeneous spaces - Dynamical systems on homogeneous spaces IV. The dynamics of billiards flows in rational polygons

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Dynamical systems. X / Viktor Vladimirovich Kozlov (2003)

Public ISBD Titre : Dynamical systems. X : general theory of vortices Type de document : texte imprimé Auteurs : Viktor Vladimirovich Kozlov, Auteur ; A. V. Ovchinnikov, Traducteur Editeur : Berlin ; London ; Cham : Springer Année de publication : 2003 Collection : Encyclopaedia of mathematical sciences num. 67 Importance : VIII, 184 p Présentation : ill. Format : 24 cm ISBN/ISSN/EAN : 978-3-540-42207-5 Note générale : Bibliogr. p. 176-180. - Index Langues : Anglais (eng) Mots-clés : Mechanics Differentiable dynamical systems Mécanique Dynamique différentiable Index. décimale : 532.5 Mouvement des liquides. Hydrodynamique. Résumé : This book contains a mathematical exposition of analogies between classical (Hamiltonian) mechanics, geometrical optics, and hydrodynamics. This theory highlights several general mathematical ideas that appeared in Hamiltonian mechanics, optics and hydrodynamics under different names. In addition, some interesting applications of the general theory of vortices are discussed in the book such as applications in numerical methods, stability theory, and the theory of exact integration of equations of dynamics. The investigation of families of trajectories of Hamiltonian systems can be reduced to problems of multidimensional ideal fluid dynamics. For example, the well-known Hamilton-Jacobi method corresponds to the case of potential flows. The book will be of great interest to researchers and postgraduate students interested in mathematical physics, mechanics, and the theory of differential equations. Well-known first-rate author Treats a major topic in mathematical physics Text: This book contains a mathematical exposition of analogies between classical (Hamiltonian) mechanics, geometrical optics, and hydrodynamics. This theory highlights several general mathematical ideas that appeared in Hamiltonian mechanics, optics and hydrodynamics under different names. In addition, some interesting applications of general vortex theory are discussed in the book such as applications in numerical methods, stability theory, and the theory of exact integration of equations of dynamics. The investigation of families of trajectories of Hamiltonian systems can be reduced to problems of multidimensional ideal fluid dynamics. For example, the well-known Hamilton-Jacobi method corresponds to the case of potential flows. The book will be of great interest to researchers and postgraduate students interested in mathematical physics, mechanics, and the theory ofdifferential equations. Note de contenu : Summary : 1. Hydrodynamics, Geometric Optics, and Classical Mechanics 2. General Vortex Theory 3. Geodesics on Lie Groups with a Left-Invariant Metric 4. Vortex Method for Integrating Hamilton Equations Supplement 1: Vorticity Invariants and Secondary Hydrodynamics Supplement 2: Quantum Mechanics and Hydrodynamics Supplement 3: Vortex Theory of Adiabatic Equilibrium Processes Dynamical systems. X : general theory of vortices [texte imprimé] / Viktor Vladimirovich Kozlov, Auteur ; A. V. Ovchinnikov, Traducteur . - Berlin ; London ; Cham : Springer, 2003 . - VIII, 184 p : ill. ; 24 cm. - (Encyclopaedia of mathematical sciences; 67) . ISBN : 978-3-540-42207-5 Bibliogr. p. 176-180. - Index Langues : Anglais (eng) Mots-clés : Mechanics Differentiable dynamical systems Mécanique Dynamique différentiable Index. décimale : 532.5 Mouvement des liquides. Hydrodynamique. Résumé : This book contains a mathematical exposition of analogies between classical (Hamiltonian) mechanics, geometrical optics, and hydrodynamics. This theory highlights several general mathematical ideas that appeared in Hamiltonian mechanics, optics and hydrodynamics under different names. In addition, some interesting applications of the general theory of vortices are discussed in the book such as applications in numerical methods, stability theory, and the theory of exact integration of equations of dynamics. The investigation of families of trajectories of Hamiltonian systems can be reduced to problems of multidimensional ideal fluid dynamics. For example, the well-known Hamilton-Jacobi method corresponds to the case of potential flows. The book will be of great interest to researchers and postgraduate students interested in mathematical physics, mechanics, and the theory of differential equations. Well-known first-rate author Treats a major topic in mathematical physics Text: This book contains a mathematical exposition of analogies between classical (Hamiltonian) mechanics, geometrical optics, and hydrodynamics. This theory highlights several general mathematical ideas that appeared in Hamiltonian mechanics, optics and hydrodynamics under different names. In addition, some interesting applications of general vortex theory are discussed in the book such as applications in numerical methods, stability theory, and the theory of exact integration of equations of dynamics. The investigation of families of trajectories of Hamiltonian systems can be reduced to problems of multidimensional ideal fluid dynamics. For example, the well-known Hamilton-Jacobi method corresponds to the case of potential flows. The book will be of great interest to researchers and postgraduate students interested in mathematical physics, mechanics, and the theory ofdifferential equations. Note de contenu : Summary : 1. Hydrodynamics, Geometric Optics, and Classical Mechanics 2. General Vortex Theory 3. Geodesics on Lie Groups with a Left-Invariant Metric 4. Vortex Method for Integrating Hamilton Equations Supplement 1: Vorticity Invariants and Secondary Hydrodynamics Supplement 2: Quantum Mechanics and Hydrodynamics Supplement 3: Vortex Theory of Adiabatic Equilibrium Processes

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General topology 3 (1995)

Public ISBD Titre : General topology 3 : paracompactness, function spaces, descriptive theory Type de document : texte imprimé Auteurs : Arhangel'skii A.V., Éditeur scientifique Editeur : Berlin ; London ; Cham : Springer Année de publication : 1995 Collection : Encyclopaedia of mathematical sciences num. Vol. 51 Importance : 232 p. Format : 25 cm ISBN/ISSN/EAN : 978-3-540-54698-6 Note générale : Bibliogr. Index Langues : Anglais (eng) Mots-clés : Topological spaces Mappings (Mathematics) Descriptive set theory Espaces topologiques Applications (mathématiques) Ensembles, Théorie descriptive des Espaces fonctionnels Index. décimale : 515.12 Topologie générale Résumé : Containing three contributions by Arhangel'skii and Choban, this book treats important topics in general topology and their role in functional analysis and axiomatic set theory. It is a useful reference for graduate students and researchers working in topology, functional analysis, set theory and probability theory Note de contenu : I. Paracompactness and Metrization. The Method of Covers in the Classification of Spaces II. Spaces of Mappings and Rings of Continuous Functions III. Descriptive Set Theory and Topology General topology 3 : paracompactness, function spaces, descriptive theory [texte imprimé] / Arhangel'skii A.V., Éditeur scientifique . - Berlin ; London ; Cham : Springer, 1995 . - 232 p. ; 25 cm. - (Encyclopaedia of mathematical sciences; Vol. 51) . ISBN : 978-3-540-54698-6 Bibliogr. Index Langues : Anglais (eng) Mots-clés : Topological spaces Mappings (Mathematics) Descriptive set theory Espaces topologiques Applications (mathématiques) Ensembles, Théorie descriptive des Espaces fonctionnels Index. décimale : 515.12 Topologie générale Résumé : Containing three contributions by Arhangel'skii and Choban, this book treats important topics in general topology and their role in functional analysis and axiomatic set theory. It is a useful reference for graduate students and researchers working in topology, functional analysis, set theory and probability theory Note de contenu : I. Paracompactness and Metrization. The Method of Covers in the Classification of Spaces II. Spaces of Mappings and Rings of Continuous Functions III. Descriptive Set Theory and Topology

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