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Providing quick and easy access to award-winning scholarship, Oxford Scholarship Online (OSO) offers access to thousands of academic monographs, in 20 subject areas across the humanities, social sciences, sciences, medicine, and law.
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Featured Book
Hyperbolic Dynamics and Brownian Motion: An Introduction
Jacques Franchi and Yves Le Jan
The idea of this book is to illustrate an interplay between distinct domains of mathematics. Firstly, this book provides an introduction to hyperbolic geometry, based on the Lorentz group PSO(1, d) and its Iwasawa decomposition, commutation relations and Haar measure, and on the hyperbolic Laplacian. The Lorentz group plays a role in relativistic space–time analogous to rotations in Euclidean space. Hyperbolic geometry is the geometry of the unit pseudo-sphere. The boundary of hyperbolic space is defined as the set of light rays. Special attention is given to the geodesic and horocyclic flows ... Read more
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