Hyperbolic Dynamics and Brownian Motion (Hardcover)
Language: English
Published by Oxford University Press, Oxford, 2012
- Hardcover
- New
Seller: CitiRetail, Stevenage, United KingdomCitiRetail
AbeBooks seller since June 29, 2022
Condition: New
£ 158.99
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Hardcover. Hyperbolic Dynamics and Brownian Motion illustrates the interplay between distinct domains of mathematics. There is no assumption that the reader is a specialist in any of these domains: only basic knowledge of linear algebra, calculus and probability theory is required.The content can be summarized in three ways:Firstly, this book provides an introduction to hyperbolic geometry, based on the Lorentz group. The Lorentzgroup plays, in relativistic space-time, a role analogue to the rotations in Euclidean space. The hyperbolic geometry is the geometry of the unit pseudo-sphere. The boundary of the hyperbolic space isdefined as the set of light rays. Special attention is given to the geodesic and horocyclic flows. Hyperbolic geometry is presented via special relativity to benefit from the physical intuition.Secondly, this book introduces basic notions of stochastic analysis: the Wiener process, Ito's stochastic integral, and calculus. This introduction allows study in linear stochastic differential equations on groups of matrices. In this way the spherical and hyperbolicBrownian motions, diffusions on the stable leaves, and the relativistic diffusion are constructed.Thirdly, quotients of the hyperbolic space under a discrete group of isometries areintroduced. In this framework some elements of hyperbolic dynamics are presented, as the ergodicity of the geodesic and horocyclic flows. This book culminates with an analysis of the chaotic behaviour of the geodesic flow, performed using stochastic analysis methods. This main result is known as Sinai's central limit theorem. A simple introduction to several important fields of modern mathematics. The exposition is based on an interplay between hyperbolic geometry, stochastic calculus, special relativity and chaotic dynamics. It is suitable for anyone with some solid background in linear algebra, calculus, and probability theory. This item is printed on demand. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability.…
Seller Inventory # 9780199654109
- Title
- Hyperbolic Dynamics and Brownian Motion (Hardcover)
- Author
- Jacques Franchi
- Publisher
- Oxford University Press, Oxford
- Publication year
- 2012
- Condition
- new
- Binding
- Hardcover
- Language
- English
- ISBN 10
- 0199654107
- ISBN 13
- 9780199654109
The content can be summarized in three ways:
Firstly, this book provides an introduction to hyperbolic geometry, based on the Lorentz group. The Lorentz group plays, in relativistic space-time, a role analogue to the rotations in Euclidean space. The hyperbolic geometry is the geometry of the unit pseudo-sphere. The boundary of the hyperbolic space is defined as the set of light rays. Special attention is given to the geodesic and horocyclic flows. Hyperbolic geometry is presented via special relativity to benefit from the physical intuition.
Secondly, this book introduces basic notions of stochastic analysis: the Wiener process, Itô's stochastic integral, and calculus. This introduction allows study in linear stochastic differential equations on groups of matrices. In this way the spherical and hyperbolic Brownian motions, diffusions on the stable leaves, and the relativistic diffusion are constructed.
Thirdly, quotients of the hyperbolic space under a discrete group of isometries are introduced. In this framework some elements of hyperbolic dynamics are presented, as the ergodicity of the geodesic and horocyclic flows. This book culminates with an analysis of the chaotic behaviour of the geodesic flow, performed using stochastic analysis methods. This main result is known as Sinai's central limit theorem.
"Synopsis" may belong to another edition of this title.
About the Author
Yves Le Jan is a professor at the University Paris-Sud of Orsay (France) and a senior member of the Institut Universitaire de France. He gave an invited talk on Probability at the ICM held in 1996 in Madrid and the Doob lecture in the 8th World Congress in Probability and Statistics held in 2012 in Istanbul.
"About the title" may belong to another edition of this title.
CitiRetail
Stevenage, United Kingdom
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