Author: Karl Endel Petersen
Publisher: Cambridge University Press
ISBN: 0521459990
Category : Ergodic theory
Languages : en
Pages : 452

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Book Description
Tutorial survey papers on important areas of ergodic theory, with related research papers.

Author: Alexander Gorodnik
Publisher: Princeton University Press
ISBN: 0691141851
Category : Mathematics
Languages : en
Pages : 136

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Book Description
The results established in this book constitute a new departure in ergodic theory and a significant expansion of its scope. Traditional ergodic theorems focused on amenable groups, and relied on the existence of an asymptotically invariant sequence in the group, the resulting maximal inequalities based on covering arguments, and the transference principle. Here, Alexander Gorodnik and Amos Nevo develop a systematic general approach to the proof of ergodic theorems for a large class of non-amenable locally compact groups and their lattice subgroups. Simple general conditions on the spectral theory of the group and the regularity of the averaging sets are formulated, which suffice to guarantee convergence to the ergodic mean. In particular, this approach gives a complete solution to the problem of establishing mean and pointwise ergodic theorems for the natural averages on semisimple algebraic groups and on their discrete lattice subgroups. Furthermore, an explicit quantitative rate of convergence to the ergodic mean is established in many cases. The topic of this volume lies at the intersection of several mathematical fields of fundamental importance. These include ergodic theory and dynamics of non-amenable groups, harmonic analysis on semisimple algebraic groups and their homogeneous spaces, quantitative non-Euclidean lattice point counting problems and their application to number theory, as well as equidistribution and non-commutative Diophantine approximation. Many examples and applications are provided in the text, demonstrating the usefulness of the results established.

Author: Boris Hasselblatt
Publisher: Springer
ISBN: 3319430599
Category : Mathematics
Languages : en
Pages : 334

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Book Description
Focussing on the mathematics related to the recent proof of ergodicity of the (Weil–Petersson) geodesic flow on a nonpositively curved space whose points are negatively curved metrics on surfaces, this book provides a broad introduction to an important current area of research. It offers original textbook-level material suitable for introductory or advanced courses as well as deep insights into the state of the art of the field, making it useful as a reference and for self-study. The first chapters introduce hyperbolic dynamics, ergodic theory and geodesic and horocycle flows, and include an English translation of Hadamard's original proof of the Stable-Manifold Theorem. An outline of the strategy, motivation and context behind the ergodicity proof is followed by a careful exposition of it (using the Hopf argument) and of the pertinent context of Teichmüller theory. Finally, some complementary lectures describe the deep connections between geodesic flows in negative curvature and Diophantine approximation.

Author: Bridget S. Webb
Publisher: Cambridge University Press
ISBN: 9780521615235
Category : Mathematics
Languages : en
Pages : 270

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Book Description
This volume provides an up-to-date overview of current research across combinatorics,.

Author: Andrew Pressley
Publisher: Cambridge University Press
ISBN: 9781139437028
Category : Mathematics
Languages : en
Pages : 246

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Book Description
This book comprises an overview of the material presented at the 1999 Durham Symposium on Quantum Groups and includes contributions from many of the world's leading figures in this area. It will be of interest to researchers and will also be useful as a reference text for graduate courses.

Author: C. M. Campbell
Publisher: Cambridge University Press
ISBN: 9780521655767
Category : Mathematics
Languages : en
Pages : 374

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Book Description
This two-volume book contains selected papers from the international conference "Groups St. Andrews 1997 in Bath". The articles are arranged in roughly alphabetical order and cover a wide spectrum of modern group theory. There are articles based on lecture courses given by five main speakers together with refereed survey and research articles contributed by other conference participants. Proceedings of earlier "Groups St. Andrews" conferences have had a major impact on the development of group theory and these volumes should be equally important.

Author: C. M. Campbell
Publisher: Cambridge University Press
ISBN: 9780521655880
Category : Group theory
Languages : en
Pages : 396

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Book Description

Author: Nicholas Young
Publisher: Cambridge University Press
ISBN: 0521705649
Category : Education
Languages : en
Pages : 370

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Book Description
A collection of articles showcasing the achievements of young Russian researchers in combinatorial and algebraic geometry and topology.

Author: Alessio Corti
Publisher: Cambridge University Press
ISBN: 9780521636414
Category : Mathematics
Languages : en
Pages : 364

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Book Description
This volume, first published in 2000, is an integrated suite of papers centred around applications of Mori theory to birational geometry.

Author: John Douglas Lamb
Publisher: Cambridge University Press
ISBN: 9780521653763
Category : Combinatorial analysis
Languages : en
Pages : 312

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Book Description
Up-to-date resource on combinatorics for graduate students and researchers.