Outer billiards on kites:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton, N.J.
Princeton University Press
[2009]
|
| Schriftenreihe: | Annals of Mathematics Studies
number 171 |
| Online-Zugang: | Volltext Volltext |
| Beschreibung: | Main description: 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 |
| Beschreibung: | 1 Online-Ressource (320 S.) |
| ISBN: | 9781400831975 |
| DOI: | 10.1515/9781400831975 |
Internformat
MARC
| LEADER | 00000nmm a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV042522580 | ||
| 003 | DE-604 | ||
| 005 | 20200331 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150423s2009 |||| o||u| ||||||eng d | ||
| 020 | |a 9781400831975 |9 978-1-4008-3197-5 | ||
| 024 | 7 | |a 10.1515/9781400831975 |2 doi | |
| 035 | |a (OCoLC)1165541061 | ||
| 035 | |a (DE-599)BVBBV042522580 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-83 | ||
| 100 | 1 | |a Schwartz, Richard Evan |d 1966- |0 (DE-588)102219111X |4 aut | |
| 245 | 1 | 0 | |a Outer billiards on kites |
| 264 | 1 | |a Princeton, N.J. |b Princeton University Press |c [2009] | |
| 264 | 4 | |c © 2009 | |
| 300 | |a 1 Online-Ressource (320 S.) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 1 | |a Annals of Mathematics Studies |v number 171 | |
| 500 | |a Main description: 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 | ||
| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe |z 978-0-691-14248-7 |
| 830 | 0 | |a Annals of Mathematics Studies |v number 171 |w (DE-604)BV040389493 |9 171 | |
| 856 | 4 | 0 | |u https://doi.org/10.1515/9781400831975?locatt=mode:legacy |x Verlag |z URL des Erstveröffentlichers |3 Volltext |
| 856 | 4 | 0 | |u http://www.degruyter.com/search?f_0=isbnissn&q_0=9781400831975&searchTitles=true |x Verlag |3 Volltext |
| 912 | |a ZDB-23-DGG |a ZDB-23-PST | ||
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027956919 | ||
Datensatz im Suchindex
| _version_ | 1804153275456421888 |
|---|---|
| any_adam_object | |
| author | Schwartz, Richard Evan 1966- |
| author_GND | (DE-588)102219111X |
| author_facet | Schwartz, Richard Evan 1966- |
| author_role | aut |
| author_sort | Schwartz, Richard Evan 1966- |
| author_variant | r e s re res |
| building | Verbundindex |
| bvnumber | BV042522580 |
| collection | ZDB-23-DGG ZDB-23-PST |
| ctrlnum | (OCoLC)1165541061 (DE-599)BVBBV042522580 |
| doi_str_mv | 10.1515/9781400831975 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02697nmm a2200361 cb4500</leader><controlfield tag="001">BV042522580</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20200331 </controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150423s2009 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781400831975</subfield><subfield code="9">978-1-4008-3197-5</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1515/9781400831975</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1165541061</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042522580</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-83</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Schwartz, Richard Evan</subfield><subfield code="d">1966-</subfield><subfield code="0">(DE-588)102219111X</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Outer billiards on kites</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Princeton, N.J.</subfield><subfield code="b">Princeton University Press</subfield><subfield code="c">[2009]</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">© 2009</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (320 S.)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Annals of Mathematics Studies</subfield><subfield code="v">number 171</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Main description: 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</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druck-Ausgabe</subfield><subfield code="z">978-0-691-14248-7</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Annals of Mathematics Studies</subfield><subfield code="v">number 171</subfield><subfield code="w">(DE-604)BV040389493</subfield><subfield code="9">171</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1515/9781400831975?locatt=mode:legacy</subfield><subfield code="x">Verlag</subfield><subfield code="z">URL des Erstveröffentlichers</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">http://www.degruyter.com/search?f_0=isbnissn&q_0=9781400831975&searchTitles=true</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-23-DGG</subfield><subfield code="a">ZDB-23-PST</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027956919</subfield></datafield></record></collection> |
| id | DE-604.BV042522580 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:24:01Z |
| institution | BVB |
| isbn | 9781400831975 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027956919 |
| oclc_num | 1165541061 |
| open_access_boolean | |
| owner | DE-83 |
| owner_facet | DE-83 |
| physical | 1 Online-Ressource (320 S.) |
| psigel | ZDB-23-DGG ZDB-23-PST |
| 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 1966- (DE-588)102219111X aut Outer billiards on kites Princeton, N.J. Princeton University Press [2009] © 2009 1 Online-Ressource (320 S.) txt rdacontent c rdamedia cr rdacarrier Annals of Mathematics Studies number 171 Main description: 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 Erscheint auch als Druck-Ausgabe 978-0-691-14248-7 Annals of Mathematics Studies number 171 (DE-604)BV040389493 171 https://doi.org/10.1515/9781400831975?locatt=mode:legacy Verlag URL des Erstveröffentlichers Volltext http://www.degruyter.com/search?f_0=isbnissn&q_0=9781400831975&searchTitles=true Verlag Volltext |
| spellingShingle | Schwartz, Richard Evan 1966- Outer billiards on kites Annals of Mathematics Studies |
| title | Outer billiards on kites |
| title_auth | Outer billiards on kites |
| title_exact_search | Outer billiards on kites |
| title_full | Outer billiards on kites |
| title_fullStr | Outer billiards on kites |
| title_full_unstemmed | Outer billiards on kites |
| title_short | Outer billiards on kites |
| title_sort | outer billiards on kites |
| url | https://doi.org/10.1515/9781400831975?locatt=mode:legacy http://www.degruyter.com/search?f_0=isbnissn&q_0=9781400831975&searchTitles=true |
| volume_link | (DE-604)BV040389493 |
| work_keys_str_mv | AT schwartzrichardevan outerbilliardsonkites |