Outer billiards on kites /:
"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 problem...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton :
Princeton University Press,
2009.
|
| Schriftenreihe: | Annals of mathematics studies ;
no. 171. |
| Schlagworte: | |
| Online-Zugang: | DE-862 DE-863 |
| Zusammenfassung: | "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 |
| Beschreibung: | 1 online resource (xii, 306 pages :) |
| Format: | Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9781400831975 1400831970 1282458582 9781282458581 9786612458583 6612458585 |
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| 245 | 1 | 0 | |a Outer billiards on kites / |c Richard Evan Schwartz. |
| 260 | |a Princeton : |b Princeton University Press, |c 2009. | ||
| 300 | |a 1 online resource (xii, 306 pages :) | ||
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| 490 | 1 | |a Annals of mathematics studies ; |v no. 171 | |
| 504 | |a Includes bibliographical references 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 fundamental orbit -- 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 | ||
| 588 | 0 | |a Print version record. | |
| 506 | |3 Use copy |f Restrictions unspecified |2 star |5 MiAaHDL | ||
| 533 | |a Electronic reproduction. |b [Place of publication not identified] : |c HathiTrust Digital Library, |d 2011. |5 MiAaHDL | ||
| 538 | |a Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. |u http://purl.oclc.org/DLF/benchrepro0212 |5 MiAaHDL | ||
| 583 | 1 | |a digitized |c 2011 |h HathiTrust Digital Library |l committed to preserve |2 pda |5 MiAaHDL | |
| 546 | |a In English. | ||
| 650 | 0 | |a Hyperbolic spaces. |0 http://id.loc.gov/authorities/subjects/sh86006874 | |
| 650 | 0 | |a Singularities (Mathematics) |0 http://id.loc.gov/authorities/subjects/sh85122871 | |
| 650 | 0 | |a Transformations (Mathematics) |0 http://id.loc.gov/authorities/subjects/sh85136920 | |
| 650 | 0 | |a Geometry, Plane. |0 http://id.loc.gov/authorities/subjects/sh85054156 | |
| 650 | 0 | |a Geometry, Modern |x Plane. |0 http://id.loc.gov/authorities/subjects/sh85054153 | |
| 650 | 6 | |a Espaces hyperboliques. | |
| 650 | 6 | |a Singularités (Mathématiques) | |
| 650 | 6 | |a Géométrie plane. | |
| 650 | 7 | |a MATHEMATICS |x Geometry |x Non-Euclidean. |2 bisacsh | |
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| 758 | |i has work: |a Outer billiards on kites (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGDqQyyW3kw7Mfy8DgfC33 |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
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| 830 | 0 | |a Annals of mathematics studies ; |v no. 171. |0 http://id.loc.gov/authorities/names/n42002129 | |
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Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn592756158 |
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| _version_ | 1826941619149996033 |
| adam_text | |
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| author | Schwartz, Richard Evan |
| author_facet | Schwartz, Richard Evan |
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| callnumber-subject | QA - Mathematics |
| collection | ZDB-4-EBA |
| contents | 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 fundamental orbit -- 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. |
| ctrlnum | (OCoLC)592756158 |
| dewey-full | 516.9 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.9 |
| dewey-search | 516.9 |
| dewey-sort | 3516.9 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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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 fundamental orbit -- 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.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="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</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Print version record.</subfield></datafield><datafield tag="506" ind1=" " ind2=" "><subfield code="3">Use copy</subfield><subfield code="f">Restrictions unspecified</subfield><subfield code="2">star</subfield><subfield code="5">MiAaHDL</subfield></datafield><datafield tag="533" ind1=" " ind2=" "><subfield code="a">Electronic reproduction.</subfield><subfield code="b">[Place of publication not identified] :</subfield><subfield code="c">HathiTrust Digital Library,</subfield><subfield code="d">2011.</subfield><subfield code="5">MiAaHDL</subfield></datafield><datafield tag="538" ind1=" " ind2=" "><subfield code="a">Master and use copy. 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| id | ZDB-4-EBA-ocn592756158 |
| illustrated | Illustrated |
| indexdate | 2025-03-18T14:14:59Z |
| institution | BVB |
| isbn | 9781400831975 1400831970 1282458582 9781282458581 9786612458583 6612458585 |
| language | English |
| oclc_num | 592756158 |
| open_access_boolean | |
| owner | MAIN DE-862 DE-BY-FWS DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-862 DE-BY-FWS DE-863 DE-BY-FWS |
| physical | 1 online resource (xii, 306 pages :) |
| psigel | ZDB-4-EBA FWS_PDA_EBA ZDB-4-EBA |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Princeton University Press, |
| record_format | marc |
| series | Annals of mathematics studies ; |
| series2 | Annals of mathematics studies ; |
| spelling | Schwartz, Richard Evan. Outer billiards on kites / Richard Evan Schwartz. Princeton : Princeton University Press, 2009. 1 online resource (xii, 306 pages :) text txt rdacontent computer c rdamedia online resource cr rdacarrier Annals of mathematics studies ; no. 171 Includes bibliographical references 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 fundamental orbit -- 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 Print version record. Use copy Restrictions unspecified star MiAaHDL Electronic reproduction. [Place of publication not identified] : HathiTrust Digital Library, 2011. MiAaHDL Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL digitized 2011 HathiTrust Digital Library committed to preserve pda MiAaHDL In English. Hyperbolic spaces. http://id.loc.gov/authorities/subjects/sh86006874 Singularities (Mathematics) http://id.loc.gov/authorities/subjects/sh85122871 Transformations (Mathematics) http://id.loc.gov/authorities/subjects/sh85136920 Geometry, Plane. http://id.loc.gov/authorities/subjects/sh85054156 Geometry, Modern Plane. http://id.loc.gov/authorities/subjects/sh85054153 Espaces hyperboliques. Singularités (Mathématiques) Géométrie plane. MATHEMATICS Geometry Non-Euclidean. bisacsh MATHEMATICS Geometry General. bisacsh Geometry, Modern Plane fast Geometry, Plane fast Hyperbolic spaces fast Singularities (Mathematics) fast Transformations (Mathematics) fast has work: Outer billiards on kites (Text) https://id.oclc.org/worldcat/entity/E39PCGDqQyyW3kw7Mfy8DgfC33 https://id.oclc.org/worldcat/ontology/hasWork Print version: Schwartz, Richard Evan. Outer billiards on kites. Princeton : Princeton University Press, 2009 9780691142494 (DLC) 2009012013 (OCoLC)317824491 Annals of mathematics studies ; no. 171. http://id.loc.gov/authorities/names/n42002129 |
| spellingShingle | Schwartz, Richard Evan Outer billiards on kites / Annals of mathematics studies ; 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 fundamental orbit -- 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. Hyperbolic spaces. http://id.loc.gov/authorities/subjects/sh86006874 Singularities (Mathematics) http://id.loc.gov/authorities/subjects/sh85122871 Transformations (Mathematics) http://id.loc.gov/authorities/subjects/sh85136920 Geometry, Plane. http://id.loc.gov/authorities/subjects/sh85054156 Geometry, Modern Plane. http://id.loc.gov/authorities/subjects/sh85054153 Espaces hyperboliques. Singularités (Mathématiques) Géométrie plane. MATHEMATICS Geometry Non-Euclidean. bisacsh MATHEMATICS Geometry General. bisacsh Geometry, Modern Plane fast Geometry, Plane fast Hyperbolic spaces fast Singularities (Mathematics) fast Transformations (Mathematics) fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh86006874 http://id.loc.gov/authorities/subjects/sh85122871 http://id.loc.gov/authorities/subjects/sh85136920 http://id.loc.gov/authorities/subjects/sh85054156 http://id.loc.gov/authorities/subjects/sh85054153 |
| title | Outer billiards on kites / |
| title_auth | Outer billiards on kites / |
| title_exact_search | Outer billiards on kites / |
| title_full | Outer billiards on kites / Richard Evan Schwartz. |
| title_fullStr | Outer billiards on kites / Richard Evan Schwartz. |
| title_full_unstemmed | Outer billiards on kites / Richard Evan Schwartz. |
| title_short | Outer billiards on kites / |
| title_sort | outer billiards on kites |
| topic | Hyperbolic spaces. http://id.loc.gov/authorities/subjects/sh86006874 Singularities (Mathematics) http://id.loc.gov/authorities/subjects/sh85122871 Transformations (Mathematics) http://id.loc.gov/authorities/subjects/sh85136920 Geometry, Plane. http://id.loc.gov/authorities/subjects/sh85054156 Geometry, Modern Plane. http://id.loc.gov/authorities/subjects/sh85054153 Espaces hyperboliques. Singularités (Mathématiques) Géométrie plane. MATHEMATICS Geometry Non-Euclidean. bisacsh MATHEMATICS Geometry General. bisacsh Geometry, Modern Plane fast Geometry, Plane fast Hyperbolic spaces fast Singularities (Mathematics) fast Transformations (Mathematics) fast |
| topic_facet | Hyperbolic spaces. Singularities (Mathematics) Transformations (Mathematics) Geometry, Plane. Geometry, Modern Plane. Espaces hyperboliques. Singularités (Mathématiques) Géométrie plane. MATHEMATICS Geometry Non-Euclidean. MATHEMATICS Geometry General. Geometry, Modern Plane Geometry, Plane Hyperbolic spaces |
| work_keys_str_mv | AT schwartzrichardevan outerbilliardsonkites |