Chaotic billiards.0821840967 Chaotic billiards billiards, any one of a number of games played with a tapered, leather-tipped stick called a cue and various numbers of balls on a rectangular, cloth-covered slate table with raised and cushioned edges. . Chernov, Nikolai and Roberto Markarian. Amer. Mathematical Society 2006 316 pages $85.00 Hardcover Mathematical surveys and monographs; v.127 QA851 In this new treatment of one of the most dynamic but difficult topics in modern theory, Chernov and Markarian keep the beginner in mind as they start from the basics and work through all the definitions and give full proofs of the main theorems This is a list of theorems, by Wikipedia page. See also
A measure of the dynamics of an attractor. Each dimension has a Lyapunov exponent. A positive exponent measures sensitive dependence on initial conditions, or how much our forecasts can diverge based upon different estimates of starting conditions. and hyperbolicity, dispersing billiards, dynamics of unstable manifolds, ergodic Adj. 1. ergodic - positive recurrent aperiodic state of stochastic systems; tending in probability to a limiting form that is independent of the initial conditions properties, statistical properties, Bunimovich billiards and general focusing chaotic billiards. Readers should have completed graduate courses in measure theory, probability, Riemann geometry, topology and complex analysis. ([c]20062005 Book News, Inc., Portland, OR) |
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