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Random Dynamical Systems by Ludwig Arnold (English) Paperback Book
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Item specifics
- Condition
- ISBN-13
- 9783642083556
- Book Title
- Random Dynamical Systems
- ISBN
- 9783642083556
- Subject Area
- Mathematics, Science
- Publication Name
- Random Dynamical Systems
- Publisher
- Springer Berlin / Heidelberg
- Item Length
- 11 in
- Subject
- Differential Equations / General, Probability & Statistics / General, System Theory, Mathematical Analysis
- Publication Year
- 2010
- Series
- Springer Monographs in Mathematics Ser.
- Type
- Textbook
- Format
- Trade Paperback
- Language
- English
- Item Weight
- 52.2 Oz
- Item Width
- 8.3 in
- Number of Pages
- Xv, 586 Pages
About this product
Product Identifiers
Publisher
Springer Berlin / Heidelberg
ISBN-10
3642083552
ISBN-13
9783642083556
eBay Product ID (ePID)
99632123
Product Key Features
Number of Pages
Xv, 586 Pages
Publication Name
Random Dynamical Systems
Language
English
Subject
Differential Equations / General, Probability & Statistics / General, System Theory, Mathematical Analysis
Publication Year
2010
Type
Textbook
Subject Area
Mathematics, Science
Series
Springer Monographs in Mathematics Ser.
Format
Trade Paperback
Dimensions
Item Weight
52.2 Oz
Item Length
11 in
Item Width
8.3 in
Additional Product Features
Intended Audience
Scholarly & Professional
Reviews
"Ludwig Arnold's monograph is going to make a very big impact for many years to come." DMV Jahresbericht, 103. Band, Heft 2, July 2001
Dewey Edition
22
Number of Volumes
1 vol.
Illustrated
Yes
Dewey Decimal
515.39
Table Of Content
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.
Synopsis
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., The first systematic presentation of the theory of dynamical systems under the influence of randomness, this book includes products of random mappings as well as random and stochastic differential equations. The basic multiplicative ergodic theorem is presented, providing a random substitute for linear algebra. On its basis, many applications are detailed. Numerous instructive examples are treated analytically or numerically.
LC Classification Number
QA299.6-433
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- t***n (2949)- Feedback left by buyer.Past 6 monthsVerified purchaseI don't give negatives; However, description was not correct; No price guide was included in this book.As you will see in book pic shown; title states price guide included, no price guide inside. Communication poor, description, no communication price guide missing from this book. Shipping time was weeks before it was even shipped. Blamed the shipping on warehouse. You own & operate a business; your warehouse is not up to standards you change who you do business with. It's your responsibility.
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