Ergodic theory, symbolic dynamics, and hyperbolic spaces
Author(s)
Bibliographic Information
Ergodic theory, symbolic dynamics, and hyperbolic spaces
（Oxford science publications）
Oxford University Press, 1991
- : pbk
Available at / 42 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
C-P||Trieste||1989.491037503
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Hokkaido University, Faculty and Graduate School of Engineering図書
: pbkdc19:515.42/er383570310463
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Note
"Bibliography" at end of each chapter
Description and Table of Contents
- Volume
-
ISBN 9780198533900
Description
This textbook provides an introductory survey to the interaction between ergodic theory and hyperbolic geometry intended for postgraduate students coming to these subjects for the first time. The aim of the volume is to explore the interplay between the two subjects and to present some of the new directions that research has taken. The chapters are all written by specialists in their respective fields and the editors have gone to great pains to ensure that the volume as a whole provides an accessible and up-to-date introduction to a very active area of research. As a result it should prove valuable to all those embarking on research in this subject as well as for those whose current research touches on topics covered here. Prerequisites are little more than a familiarity with the basics of topology, analysis, and group theory as might be gained from an undergraduate degree course. Early chapters present an introduction to the fundamental concepts of hyperbolic geometry and ergodic theory.
Subsequent chapters develop more advanced topics such as explicit coding methods, symbolic dynamics, the theory of nuclear operators as applied to the Ruelle-Perron-Frobenius (or transfer) operator, the Patterson measure, and the connections with finiteness phenomena in the structure of hyperbolic spaces.
- Volume
-
: pbk ISBN 9780198596851
Description
This textbook provides an introductory survey to the interaction between ergodic theory and hyperbolic geometry intended for postgraduate students coming to these subjects for the first time. The aim of the volume is to explore the interplay between the two subjects and to present some of the new directions that research has taken. The chapters are all written by specialists in their respective fields and the editors have gone to great pains to ensure that the volume as a whole provides an accessible and up-to-date introduction to a very active area of research. As a result it should prove valuable to all those embarking on research in this subject as well as for those whose current research touches on topics covered here. Prerequisites are little more than a familiarity with the basics of topology, analysis, and group theory as might be gained from an undergraduate degree course. Early chapters present an introduction to the fundamental concepts of hyperbolic geometry and ergodic theory.
Subsequent chapters develop more advanced topics such as explicit coding methods, symbolic dynamics, the theory of nuclear operators as applied to the Ruelle-Perron-Frobenius (or transfer) operator, the Patterson measure, and the connections with finiteness phenomena in the structure of hyperbolic spaces.
Table of Contents
- Alan F. Beardon: An introduction to hyperbolic geometry
- Michael Keane: Ergodic theory and subshifts of finite type
- Anthony Manning: Dynamics of geodesic and horocycle flows on surfaces of constant negative curvature
- Roy L. Adler: Geodesic flows, interval maps, and symbolic dynamics
- Caroline Series: Geometrical methods of symbolic coding
- Mark Pollicott: Closed geodesics and zeta functions
- Dieter H. Mayer: Continued fractions and related transformations
- Steven P. Lalley: Probabilistic methods in certain counting problems of ergodic theory
- Peter J. Nicholls: A measure on the limit set of a discrete group
- Etienne Ghys & Pierre de la Harpe: Infinite groups as geometric objects (after Gromov)
- James W. Cannon: The theory of negatively curved spaces and groups
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