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This text is a rigorous introduction to ergodic theory, developing the machinery of conditional measures and expectations, mixing, and recurrence.

Beginning by developing the basics of ergodic theory and progressing to describe some recent applications to number theory, this book goes beyond the standard texts in this topic. Applications include Weyl's polynomial equidistribution theorem, the ergodic proof of Szemeredi's theorem, the connection between the continued fraction map and the modular surface, and a proof of the equidistribution of horocycle orbits.

*Ergodic Theory with a view towards Number Theory* will appeal to mathematicians with some standard background in measure theory and functional analysis. No background in ergodic theory or Lie theory is assumed, and a number of exercises and hints to problems are included, making this the perfect companion for graduate students and researchers in ergodic theory, homogenous dynamics or number theory.

- Series:
**259** - Author:
**Manfred Einsiedler, Thomas Ward (auth.)** - Year:
**2011** - Publisher:
**Springer-Verlag London** - Language:
**English** - ISBN:
**0857290207,9780857290205**

- File size:
**3 365 745** - Format:
**pdf**

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This text is a rigorous introduction to ergodic theory, developing the machinery of conditional measures and expectations, mixing, and recurrence. Beginning by developing the basics of ergodic theory and progressing to describe some recent applications to...

This volume of proceedings is an offspring of the special semester Ergodic Theory, Geometric Rigidity and Number Theory which was held at the Isaac Newton Institute for Mathematical Sciences in Cambridge, UK, from JanÂ uary until July, 2000. Beside the ac...

Following the concept of the EMS series this volume sets out to familiarize the reader to the fundamental ideas and results of modern ergodic theory and to its applications to dynamical systems and statistical mechanics. The exposition starts from the bas...

Following the concept of the EMS series this volume sets out to familiarize the reader to the fundamental ideas and results of modern ergodic theory and to its applications to dynamical systems and statistical mechanics. The exposition starts from the bas...

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 s...

This book is an introduction to the ergodic theory behind common number expansions, for instance decimal expansions, continued fractions and many others. The questions studied are dynamical as well as number theoretic in nature, and the answers are obtain...

This book is based on a course given at the University of Chicago in 1980-81. As with the course, the main motivation of this work is to present an accessible treatment, assuming minimal background, of the profound work of G. A. Margulis concerning rigidi...

This second edition updates the well-regarded 2001 publication with new short sections on topics like Catalan numbers and their relationship to Pascal's triangle and Mersenne numbers, Pollard rho factorization method, Hoggatt-Hensell identity. Koshy has a...

The aim of this series is to inform both professional philosophers and a larger readership (of social and natural scientists, methodologists, mathematicians, students, teachers, publishers, etc. ) about what is going on, who's who, and who does what in co...

The sixteenth annual symposium of the Society for the Study of Inborn Errors of Metabolism was held in Bristol from 12th to 14th July, 1978. About 25 invited speakers and 150 participants came from many parts of Europe and North America to consider the to...

For some years I have felt there was a need for a single, comprehenÂ sive, reference book on exploration geology. Numerous textbooks are available on subjects such as geophysical prospecting, exploration geochemistry, mining geology, photogeology and gene...

In September 1977 a "Regional Science Symposium" was held at the Faculty of Economics of the University of Goningen in the Netherlands. The impetus in organizing this symposium was the recent estabÂ lishmen t at the F acuIty of Economics of a group engage...

While general systems research has had a considerable impact on research in the social sciences, this impact has been mainly conceptual and has not served to provide the operational and methodological aids for research which are possible. In addition, man...

Project Set Strategies focuses on an issue of vital concern to corporate managers: the development and implementation of strategy. Regretfully, this topic has received too little attention in the literature of finance and has been treated inÂ completely i...

The productive work of widely distributed academic research has contributed substantially, over the postwar period, to important advances in our understanding. It has also offered a clearer recognition of many unresolved problems. NeverÂ theless, the prog...

''The problem of Transcendence is the problem of our time. " I Needless to say, Transcendence was a particularly lively i~sue when Karl Heim wrote these words in the mid-1930's. Within the province of philosophiÂ cal theology and philosophy of religion, h...

It is my hope that this publication of a "lost" work by Galiani will interest scholars of many nations and disciplines. Few writers could make a more compelling claim upon such a cosmopolitan audience. An Italian with deep roots in his homeland, Galiani a...

This liber amicorum honours Professor Jan Tissot van Patot as a scholar, referring in particular to his concern with transport economics. The signiÂ ficance of his work grew out of his influence within Netherlands Railways as, with the passage of the year...