Springer eBooks may be purchased by end-customers only and are sold without copy protection (DRM free). Instead, all eBooks include personalized watermarks. This means you can read the Springer eBooks across numerous devices such as Laptops, eReaders, and tablets.
You can pay for Springer eBooks with Visa, Mastercard, American Express or Paypal.
After the purchase you can directly download the eBook file or read it online in our Springer eBook Reader. Furthermore your eBook will be stored in your MySpringer account. So you can always re-download your eBooks.
digitally watermarked, no DRM
The eBook version of this title will be available soon
This book studies ergodic-theoretic aspects of random dynam- ical systems, i.e. of deterministic systems with noise. It aims to present a systematic treatment of a series of recent results concerning invariant measures, entropy and Lyapunov exponents of such systems, and can be viewed as an update of Kifer's book. An entropy formula of Pesin's type occupies the central part. The introduction of relation numbers (ch.2) is original and most methods involved in the book are canonical in dynamical systems or measure theory. The book is intended for people interested in noise-perturbed dynam- ical systems, and can pave the way to further study of the subject. Reasonable knowledge of differential geometry, measure theory, ergodic theory, dynamical systems and preferably random processes is assumed.
Content Level »Research
Keywords »Ergodic theory - diffeomorphism - differential geometry - manifold - measure - measure theory - random dynamical system
Preliminaries.- Entropy and Lyapunov exponents of random diffeomorphisms.- Estimation of entropy from above through Lyapunov exponents.- Stable invariant manifolds of random diffeomorphisms.- Estimation of entropy from below through Lyapunov exponents.- Stochastic flows of diffeomorphisms.- Characterization of measures satisfying entropy formula.- Random perturbations of hyperbolic attractors.