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Dynamical Billiards
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2015 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [sv]

Följande rapport behandlar matematiska biljarder. Matematiska biljarder är en idealisering av det välkända spelet, dar en punktmassa (biljardbollen) är begransad till ett område (biljardbordet) via elastiska kollisioner. Teorin används inom tillämpade omraden såsom mekanik och geometrisk optik, men fungerar även som en testarena för matematikers teorier. Rapporten betraktar biljarder från ett dynamiska system-perspektiv där olika aspekter av teorin tas upp med illustrerande bilder. Läsaren introduceras till teorin via två exempel; cirkeln och kvadraten med tillämpningar. Därefter undersöks mer generella konvexa biljardbord samt slutligen kopplingen till vridande avbildningar (twist maps) ochinvarianta kurvor. Rapporten baseras på bentliga texter i ämnet.

Abstract [en]

This paper is devoted to mathematical billiards. Mathematical billiards is an idealization of the well known game, where the point mass (the billiard ball) is conned in a domain (the billiard board) through elastic collisions. The theory finds various applications in applied fields such as mechanics and geometrical optics, but also serves as a playground for mathematicians to test their theories. The paper will consider billiards from a dynamical systems point of view, presenting various aspects of the theory supplied with pictures for intuition. The reader is introduced to the theory through two examples: the circle and the square with applications. General convex billiards are then considered and finally the link with twist maps and invariant curves. The theory is based on texts in the field.

Place, publisher, year, edition, pages
2015.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-168083OAI: oai:DiVA.org:kth-168083DiVA: diva2:814270
Supervisors
Available from: 2015-05-26 Created: 2015-05-26 Last updated: 2015-05-26Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
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Output format
  • html
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