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Books > Science & Mathematics > Mathematics > Applied mathematics > Chaos theory
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Introduction To Mathematical Billiards, An (Hardcover)
Loot Price: R2,730
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Introduction To Mathematical Billiards, An (Hardcover)
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'This book offers one of the few places where a collection of
results from the literature can be found ... The book has an
extensive bibliography ... It is very nice to have the compendium
of results that is presented here.'zbMATHA mathematical billiard is
a mechanical system consisting of a billiard ball on a table of any
form (which can be planar or even a multidimensional domain) but
without billiard pockets. The ball moves and its trajectory is
defined by the ball's initial position and its initial speed
vector. The ball's reflections from the boundary of the table are
assumed to have the property that the reflection and incidence
angles are the same. This book comprehensively presents known
results on the behavior of a trajectory of a billiard ball on a
planar table (having one of the following forms: circle, ellipse,
triangle, rectangle, polygon and some general convex domains). It
provides a systematic review of the theory of dynamical systems,
with a concise presentation of billiards in elementary mathematics
and simple billiards related to geometry and physics.The
description of these trajectories leads to the solution of various
questions in mathematics and mechanics: problems related to liquid
transfusion, lighting of mirror rooms, crushing of stones in a
kidney, collisions of gas particles, etc. The analysis of billiard
trajectories can involve methods of geometry, dynamical systems,
and ergodic theory, as well as methods of theoretical physics and
mechanics, which has applications in the fields of biology,
mathematics, medicine, and physics.
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