Download E-books Outer Billiards on Kites (AM-171) (Annals of Mathematics Studies) PDF

By Richard Evan Schwartz

Outer billiards is a uncomplicated dynamical approach outlined relative to a convex form within the aircraft. B. H. Neumann brought the program within the Fifties, and J. Moser popularized it as a toy version for celestial mechanics. All alongside, the so-called Moser-Neumann query has been one of many crucial difficulties within the box. this query asks even if one could have an outer billiards method with an unbounded orbit. The Moser-Neumann query is an idealized model of the query of no matter if, as a result of small disturbances in its orbit, the Earth can get away of its orbit and fly clear of the sunlight. In Outer Billiards on Kites, Richard Schwartz provides his affirmative option to the Moser-Neumann challenge. He exhibits that an outer billiards approach could have an unbounded orbit whilst outlined relative to any irrational kite. A kite is a quadrilateral having a diagonal that may be a line of bilateral symmetry. The kite is irrational if the opposite diagonal divides the quadrilateral into triangles whose components should not rationally similar. as well as fixing the elemental challenge, Schwartz relates outer billiards on kites to such subject matters as Diophantine approximation, the modular team, self-similar units, polytope trade maps, profinite completions of the integers, and solenoids--connections that jointly let for a reasonably entire research of the dynamical system.

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