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Dynamical Systems and Processes
Michel Weber, University Louis Pasteur et CNRS, Strasbourg, France
A publication of the European Mathematical Society.
cover
IRMA Lectures in Mathematics and Theoretical Physics
2009; 773 pp; hardcover
Volume: 14
ISBN-10: 3-03719-046-9
ISBN-13: 978-3-03719-046-3
List Price: US$128
Member Price: US$102.40
Order Code: EMSILMTP/14
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This book presents in a concise and accessible way, as well as in a common setting, various tools and methods arising from spectral theory, ergodic theory and stochastic processes theory, which form the basis of and contribute interactively a great deal to the current research on almost-everywhere convergence problems.

Researchers working in dynamical systems and at the crossroads of spectral theory, ergodic theory and stochastic processes will find the tools, methods, and results presented in this book of great interest. It is written in a style accessible to graduate students.

A publication of the European Mathematical Society. Distributed within the Americas by the American Mathematical Society.

Readership

Graduate students and research mathematicians interested in dynamical systems.

Table of Contents

Part I. Spectral theorems and convergence in mean
  • The von Neumann theorem and spectral regularization
  • Spectral representation of weakly stationary processes
Part II. Ergodic theorems
  • Dynamical systems--ergodicity and mixing
  • Pointwise ergodic theorems
  • Banach principle and continuity principle
  • Maximal operators and Gaussian processes
  • The central limit theorem for dynamical systems
Part III. Methods arising from the theory of stochastic processes
  • The metric entropy method
  • The majorizing measure method
  • Gaussian processes
Part IV. Three studies
  • Riemann sums
  • A study of the system \((f(nx))\)
  • Divisors and random walks
  • Bibliography
  • Index
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