CiNii 図書 - Ergodic theory, symbolic dynamics, and hyperbolic spaces

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.

巻冊次: : pbk ISBN 9780198596851

内容説明

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.

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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Ergodic theory, symbolic dynamics, and hyperbolic spaces

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