Random Dynamical Systems
1st Edition
Published on 13. November 2002
Book
Hardback
XV, 586 pages
978-3-540-63758-5 (ISBN)
Description
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.
Reviews / Votes
"Ludwig Arnold's monograph is going to make a very big impact for many years to come." DMV Jahresbericht, 103. Band, Heft 2, July 2001More details
Product info
Book
Series
Edition
1st.ed 1998. Corr. 2nd printing
Language
English
Place of publication
Berlin, Heidelberg
Germany
Target group
Research
Edition type
Revised edition
Product notice
Laminated cover
Illustrations
40 Abb.
Dimensions
Height: 243 mm
Width: 193 mm
Thickness: 41 mm
Weight
1044 gr
ISBN-13
978-3-540-63758-5 (9783540637585)
DOI
10.1007/978-3-662-12878-7
Schweitzer Classification
Other editions
Additional editions
Ludwig Arnold
Random Dynamical Systems
Book
12/2010
1st Edition
Springer
€139.09
Shipment within 7-9 days
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.