Overview

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.

Full Product Details

Author:   Ludwig Arnold
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   1st.ed 1998. Corr. 2nd printing 2002
Dimensions:   Width: 15.50cm , Height: 3.30cm , Length: 23.50cm
Weight:   2.270kg
ISBN:  

9783540637585

ISBN 10:   3540637583
Pages:   586
Publication Date:   19 August 1998
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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"""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"

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

Ludwig Arnold's monograph is going to make a very big impact for many years to come. <br> DMV Jahresbericht, 103. Band, Heft 2, July 2001

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