Logo - springer
Slogan - springer

Mathematics - Dynamical Systems & Differential Equations | Distance Expanding Random Mappings, Thermodynamical Formalism, Gibbs Measures and Fractal Geometry

Distance Expanding Random Mappings, Thermodynamical Formalism, Gibbs Measures and Fractal Geometry

Series: Lecture Notes in Mathematics, Vol. 2036

Mayer, Volker, Skorulski, Bartlomiej, Urbanski, Mariusz

2011, X, 112p. 3 illus. in color.

Available Formats:
eBook
Information

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.

 
$39.95

(net) price for USA

ISBN 978-3-642-23650-1

digitally watermarked, no DRM

Included Format: PDF and EPUB

download immediately after purchase


learn more about Springer eBooks

add to marked items

Softcover
Information

Softcover (also known as softback) version.

You can pay for Springer Books with Visa, Mastercard, American Express or Paypal.

Standard shipping is free of charge for individual customers.

 
$49.95

(net) price for USA

ISBN 978-3-642-23649-5

free shipping for individuals worldwide

usually dispatched within 3 to 5 business days


add to marked items

  • About this book

  • Contains new results
  • Complete treatment of the topic
  • Originality of the topic
The theory of random dynamical systems originated from stochastic
differential equations. It is intended to provide a framework and
techniques to describe and analyze the evolution of dynamical
systems when the input and output data are known only approximately, according to some probability distribution. The development of this field, in both the theory and applications, has gone in many directions. In this manuscript we introduce measurable expanding random dynamical systems, develop the thermodynamical formalism and establish, in particular, the exponential decay of correlations and analyticity of the expected pressure although the spectral gap property does not hold. This theory is then used to investigate fractal properties of conformal random systems. We prove a Bowen’s formula and develop the multifractal formalism of the Gibbs states. Depending on the behavior of the Birkhoff sums of the pressure function we arrive at a natural classification of the systems into two classes: quasi-deterministic systems, which share many
properties of deterministic ones; and essentially random systems, which are rather generic and never bi-Lipschitz equivalent to deterministic systems. We show that in the essentially random case the Hausdorff measure vanishes, which refutes a conjecture by Bogenschutz and Ochs. Lastly, we present applications of our results to various specific conformal random systems and positively answer a question posed by Bruck and Buger concerning the Hausdorff dimension of quadratic random Julia sets.

Content Level » Research

Keywords » 37-XX - Hausdorff dimension - multifractal spectrum - random dynamical systems - thermodynamical formalism

Related subjects » Dynamical Systems & Differential Equations

Table of contents / Preface / Sample pages 

Popular Content within this publication 

 

Articles

Read this Book on Springerlink

Services for this book

New Book Alert

Get alerted on new Springer publications in the subject area of Dynamical Systems and Ergodic Theory.