Basic Ergodic Theory [paperback] Nadkarni, M.G. [Jan 01, 1995]

Basic Ergodic Theory

Science & Math

Nadkarni, M.G.

Mathematics

Hindustan Book Agency

<p>This book treats some basic topics in the spectral theory of dynamical systems. The treatment is at a general level, but two more advanced theorems, one by H. Helson and W. Parry and the other by B. Host, are presented. Moreover, Ornstein's family of mixing rank one automorphisms is described with construction and proof. Systems of imprimitivity and their relevance to ergodic theory are discussed, and Baire category theorems of ergodic theory, scattered in the literature, are derived in a unified way. Riesz products are considered and they are used to describe the spectral types and eigenvalues of rank one automorphisms.</p>

Spectral Theory of Dynamical Systems (Text and Readings in Mathematics)

Amer Mathematical Society

<p>This is an introductory book on Ergodic Theory. The presentation has a slow pace and the book can be read by any person with a background in basic measure theory and metric topology. A new feature of the book is that the basic topics of Ergodic Theory such as the Poincare recurrence lemma, induced automorphisms and Kakutani towers, compressibility and E. Hopf's theorem, the theorem of Ambrose on representation of flows are treated at the descriptive set-theoretic level before their measure-theoretic or topological versions are presented. In addition, topics around the Glimm-Effros theorem are discussed. In the third edition a chapter entitled 'Additional Topics' has been added. It gives Liouville's Theorem on the existence of invariant measure, entropy theory leading up to Kolmogorov-Sinai Theorem, and the topological dynamics proof of van der Waerden's theorem on arithmetical progressions.</p>

Basic ergodic theory (Texts and Readings in Mathematics)

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Books by Nadkarni, M.G.

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Basic Ergodic Theory

Spectral Theory of Dynamical Systems (Text and Readings in Mathematics)

Basic ergodic theory (Texts and Readings in Mathematics)