Hyperbolic Dynamics Brownian Motion by Franchi Jacques (11 results)

Hardcover. Condition: Very Good. No Jacket. May have limited writing in cover pages. Pages are unmarked. ~ ThriftBooks: Read More, Spend Less.

Hardcover. Condition: Fine. Dust Jacket Condition: No Dust Jacket As Issued. A nice, bright copy. ; Oxford Mathematical Monographs; 9.53 X 6.50 X 0.79 inches; 266 pages.

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Hardcover. Condition: new. 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.…