Outer Billiards on Kites (Annals of Mathematics Studies) 在线电子书 pdf 下载 txt下载 epub 下载 mobi 下载 2024

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Richard Evan Schwartz 作者

Princeton University Press

译者

2009-10-20 出版日期

312 页数

USD 45.00 价格

Paperback

Annals of Mathematics Studies 丛书系列

9780691142494 图书编码

Outer Billiards on Kites (Annals of Mathematics Studies) 在线电子书图书标签: 数学

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Outer Billiards on Kites (Annals of Mathematics Studies) 在线电子书 epub 下载 mobi 下载 pdf 下载 txt 下载 2024

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Outer billiards is a basic dynamical system defined relative to a convex shape in the plane. B.H. Neumann introduced this system in the 1950s, and J. Moser popularized it as a toy model for celestial mechanics. All along, the so-called Moser-Neumann question has been one of the central problems in the field. This question asks whether or not one can have an outer billiards system with an unbounded orbit. The Moser-Neumann question is an idealized version of the question of whether, because of small disturbances in its orbit, the Earth can break out of its orbit and fly away from the Sun. In "Outer Billiards on Kites", Richard Schwartz presents his affirmative solution to the Moser-Neumann problem. He shows that an outer billiards system can have an unbounded orbit when defined relative to any irrational kite. A kite is a quadrilateral having a diagonal that is a line of bilateral symmetry. The kite is irrational if the other diagonal divides the quadrilateral into two triangles whose areas are not rationally related. In addition to solving the basic problem, Schwartz relates outer billiards on kites to such topics as Diophantine approximation, the modular group, self-similar sets, polytope exchange maps, profinite completions of the integers, and solenoids - connections that together allow for a fairly complete analysis of the dynamical system.

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