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Outer billiards on kites /

Schwartz, Richard Evan.

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Outer billiards on kites /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Outer billiards on kites // Richard Evan Schwartz.
Author:	Schwartz, Richard Evan.
Published:	Princeton :Princeton University Press, : 2009.,
Description:	xii, 306 p. :ill. ;24 cm.
[NT 15003449]:	Introduction -- The arithmetic graph -- The hexagrid theorem -- Period copying -- Proof of the erratic orbits theorem -- The master picture theorem -- The pinwheel lemma -- The torus lemma -- The strip functions -- Proof of the master picture theorem -- Proof of the embedding theorem -- Extension and symmetry -- Proof of hexagrid theorem I -- The barrier theorem -- Proof of hexagrid theorem II -- Proof of the intersection lemma -- Diophantine approximation -- The diophantine lemma -- The decomposition theorem -- Existence of strong sequences -- Structure of the inferior and superior sequences -- The comet theorem -- Dynamical consequences -- Geometric consequences -- Proof of the copy theorem -- Pivot arcs in the even case -- Proof of the pivot theorem -- Proof of the period theorem -- Hovering components -- Proof of the low vertex theorem -- Structure of periodic points -- Self-similarity -- General orbits on kites -- General quadrilaterals.
Subject:	Hyperbolic spaces. -
Online resource:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=018701938&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
ISBN:	9780691142494 (pbk. : alk. paper) :

Outer billiards on kites /
Schwartz, Richard Evan.

Outer billiards on kites /Richard Evan Schwartz. - Princeton :Princeton University Press,2009. - xii, 306 p. :ill. ;24 cm. - Annals of mathematics studies ;no. 171. - Annals of mathematics studies ;no. 174..

Includes bibliographical references (p. [303]-304) and index.

Introduction -- The arithmetic graph -- The hexagrid theorem -- Period copying -- Proof of the erratic orbits theorem -- The master picture theorem -- The pinwheel lemma -- The torus lemma -- The strip functions -- Proof of the master picture theorem -- Proof of the embedding theorem -- Extension and symmetry -- Proof of hexagrid theorem I -- The barrier theorem -- Proof of hexagrid theorem II -- Proof of the intersection lemma -- Diophantine approximation -- The diophantine lemma -- The decomposition theorem -- Existence of strong sequences -- Structure of the inferior and superior sequences -- The comet theorem -- Dynamical consequences -- Geometric consequences -- Proof of the copy theorem -- Pivot arcs in the even case -- Proof of the pivot theorem -- Proof of the period theorem -- Hovering components -- Proof of the low vertex theorem -- Structure of periodic points -- Self-similarity -- General orbits on kites -- General quadrilaterals.

"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."--Publisher website.

ISBN: 9780691142494 (pbk. : alk. paper) :US45.00

LCCN: 2009012013

Nat. Bib. No.: GBA979004bnb

Nat. Bib. Agency Control No.: 015346788UkSubjects--Topical Terms:

555726
Hyperbolic spaces.

LC Class. No.: QA685 / .S45 2009

Dewey Class. No.: 516.9

Outer billiards on kites /
LDR:03466cam 2200301 a 4500 001 975183
003 DLC
005 20100809162913.0
008 111017s2009 njua b 001 0 eng
010 $a 2009012013
015 $a GBA979004 $2 bnb
016 7 $a 015346788 $2 Uk
020 $a 9780691142494 (pbk. : alk. paper) : $c US45.00
020 $a 0691142491 (pbk. : alk. paper)
020 $a 9780691142487 (hardcover : alk. paper)
020 $a 0691142483 (hardcover : alk. paper)
035 $a (OCoLC)ocn317824491
035 $a AS-BW-100-N-01
040 $a DLC $b eng $c DLC $d BTCTA $d UKM $d C#P $d ILU $d DEBBG $d OCL $d CDX $d OCL $d DLC
050 0 0 $a QA685 $b .S45 2009
082 0 0 $a 516.9 $2 22
100 1 $a Schwartz, Richard Evan. $3 922835
245 1 0 $a Outer billiards on kites / $c Richard Evan Schwartz.
260 # $a Princeton : $b Princeton University Press, $c 2009.
300 $a xii, 306 p. : $b ill. ; $c 24 cm.
490 1 $a Annals of mathematics studies ; $v no. 171
504 $a Includes bibliographical references (p. [303]-304) and index.
505 0 # $a Introduction -- The arithmetic graph -- The hexagrid theorem -- Period copying -- Proof of the erratic orbits theorem -- The master picture theorem -- The pinwheel lemma -- The torus lemma -- The strip functions -- Proof of the master picture theorem -- Proof of the embedding theorem -- Extension and symmetry -- Proof of hexagrid theorem I -- The barrier theorem -- Proof of hexagrid theorem II -- Proof of the intersection lemma -- Diophantine approximation -- The diophantine lemma -- The decomposition theorem -- Existence of strong sequences -- Structure of the inferior and superior sequences -- The comet theorem -- Dynamical consequences -- Geometric consequences -- Proof of the copy theorem -- Pivot arcs in the even case -- Proof of the pivot theorem -- Proof of the period theorem -- Hovering components -- Proof of the low vertex theorem -- Structure of periodic points -- Self-similarity -- General orbits on kites -- General quadrilaterals.
520 # $a "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."--Publisher website.
650 # 0 $a Hyperbolic spaces. $3 555726
650 # 0 $a Singularities (Mathematics) $3 588970
650 # 0 $a Transformations (Mathematics) $3 544232
650 # 0 $a Geometry, Plane. $3 579180
830 0 $a Annals of mathematics studies ; $v no. 174. $3 1299119
856 4 1 $3 Table of contents $u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=018701938&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA