| 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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536 Chaleur.Thermodynamique 
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