Dekorationsartikel gehören nicht zum Leistungsumfang.
Random Dynamical Systems
Taschenbuch von Ludwig Arnold
Sprache: Englisch

118,95 €*

inkl. MwSt.

Versandkostenfrei per Post / DHL

Lieferzeit 4-7 Werktage

Kategorien:
Beschreibung
Background and Scope of the Book This book continues, extends, and unites various developments in the intersection of probability theory and dynamical systems. I will briefly outline the background of the book, thus placing it in a systematic and historical context and tradition. Roughly speaking, a random dynamical system is a combination of a measure-preserving dynamical system in the sense of ergodic theory, (D,F,lP', (B(t))tE'lf), 'II'= JR+, IR, z+, Z, with a smooth (or topological) dy­ namical system, typically generated by a differential or difference equation :i: = f(x) or Xn+l = tp(x.,), to a random differential equation :i: = f(B(t)w,x) or random difference equation Xn+l = tp(B(n)w, Xn)· Both components have been very well investigated separately. However, a symbiosis of them leads to a new research program which has only partly been carried out. As we will see, it also leads to new problems which do not emerge if one only looks at ergodic theory and smooth or topological dynam­ ics separately. From a dynamical systems point of view this book just deals with those dynamical systems that have a measure-preserving dynamical system as a factor (or, the other way around, are extensions of such a factor). As there is an invariant measure on the factor, ergodic theory is always involved.
Background and Scope of the Book This book continues, extends, and unites various developments in the intersection of probability theory and dynamical systems. I will briefly outline the background of the book, thus placing it in a systematic and historical context and tradition. Roughly speaking, a random dynamical system is a combination of a measure-preserving dynamical system in the sense of ergodic theory, (D,F,lP', (B(t))tE'lf), 'II'= JR+, IR, z+, Z, with a smooth (or topological) dy­ namical system, typically generated by a differential or difference equation :i: = f(x) or Xn+l = tp(x.,), to a random differential equation :i: = f(B(t)w,x) or random difference equation Xn+l = tp(B(n)w, Xn)· Both components have been very well investigated separately. However, a symbiosis of them leads to a new research program which has only partly been carried out. As we will see, it also leads to new problems which do not emerge if one only looks at ergodic theory and smooth or topological dynam­ ics separately. From a dynamical systems point of view this book just deals with those dynamical systems that have a measure-preserving dynamical system as a factor (or, the other way around, are extensions of such a factor). As there is an invariant measure on the factor, ergodic theory is always involved.
Zusammenfassung
Dies ist die erste umfassende Monographie zu diesem aktiven Gebiet. Es beginnt bei den Grundlagen und schließt aktuelle Forschung ebenso mit ein.Es ist von einem der führenden Köpfe auf diesem Gebiet geschrieben. .
Inhaltsverzeichnis
I. Random Dynamical Systems and Their Generators.- 1. Basic Definitions. Invariant Measures.- 2. Generation.- II. Multiplicative Ergodic Theory.- 3. The Multiplicative Ergodic Theorem in Euclidean Space.- 4. The Multiplicative Ergodic Theorem on Bundles and Manifolds.- 5. The MET for Related Linear and Affine RDS.- 6. RDS on Homogeneous Spaces of the General Linear Group.- III. Smooth Random Dynamical Systems.- 7. Invariant Manifolds.- 8. Normal Forms.- 9. Bifurcation Theory.- IV. Appendices.- Appendix A. Measurable Dynamical Systems.- A.1 Ergodic Theory.- A.2 Stochastic Processes and Dynamical Systems.- A.3 Stationary Processes.- A.4 Markov Processes.- Appendix B. Smooth Dynamical Systems.- B.1 Two-Parameter Flows on a Manifold.- B.4 Autonomous Case: Dynamical Systems.- B.5 Vector Fields and Flows on Manifolds.- References.
Details
Erscheinungsjahr: 2010
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 608
Reihe: Springer Monographs in Mathematics
Inhalt: xv
586 S.
ISBN-13: 9783642083556
ISBN-10: 3642083552
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Arnold, Ludwig
Auflage: Softcover reprint of hardcover 1st ed. 1998
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Springer Monographs in Mathematics
Maße: 279 x 210 x 33 mm
Von/Mit: Ludwig Arnold
Erscheinungsdatum: 15.12.2010
Gewicht: 1,46 kg
preigu-id: 107167231
Zusammenfassung
Dies ist die erste umfassende Monographie zu diesem aktiven Gebiet. Es beginnt bei den Grundlagen und schließt aktuelle Forschung ebenso mit ein.Es ist von einem der führenden Köpfe auf diesem Gebiet geschrieben. .
Inhaltsverzeichnis
I. Random Dynamical Systems and Their Generators.- 1. Basic Definitions. Invariant Measures.- 2. Generation.- II. Multiplicative Ergodic Theory.- 3. The Multiplicative Ergodic Theorem in Euclidean Space.- 4. The Multiplicative Ergodic Theorem on Bundles and Manifolds.- 5. The MET for Related Linear and Affine RDS.- 6. RDS on Homogeneous Spaces of the General Linear Group.- III. Smooth Random Dynamical Systems.- 7. Invariant Manifolds.- 8. Normal Forms.- 9. Bifurcation Theory.- IV. Appendices.- Appendix A. Measurable Dynamical Systems.- A.1 Ergodic Theory.- A.2 Stochastic Processes and Dynamical Systems.- A.3 Stationary Processes.- A.4 Markov Processes.- Appendix B. Smooth Dynamical Systems.- B.1 Two-Parameter Flows on a Manifold.- B.4 Autonomous Case: Dynamical Systems.- B.5 Vector Fields and Flows on Manifolds.- References.
Details
Erscheinungsjahr: 2010
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 608
Reihe: Springer Monographs in Mathematics
Inhalt: xv
586 S.
ISBN-13: 9783642083556
ISBN-10: 3642083552
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Arnold, Ludwig
Auflage: Softcover reprint of hardcover 1st ed. 1998
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Springer Monographs in Mathematics
Maße: 279 x 210 x 33 mm
Von/Mit: Ludwig Arnold
Erscheinungsdatum: 15.12.2010
Gewicht: 1,46 kg
preigu-id: 107167231
Warnhinweis

Ähnliche Produkte

Ähnliche Produkte