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A Survey of Dynamical Billiards
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2013 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

In this report we will present the basic concepts and results of the theory of dynamical billiards

which idealizes the concept of a volumeless ball re ecting against the inside of a billiard table

without friction.This motion will continue indenitely and it is of interest to study its behaviour.

We will show that the study of a billiard system can be reduced to the study of an associated

map called the billiard map dened on a cylindrical phase space. Using this formalism the

specic systems where the billiard table is given by a circle, right iscoceles triangle and ellipse

will be studied in some detail along with the existence of peridic points through Birkho's

famous theorem and some more novel results such as an instance of Benford's law regarding

the distribution of rst digits in real-life data. We will also dene the concept of a caustic

and investigate their existence and non-existence which will lead us to the concept of circle

homeomorphisms and will also provide the opportunity to illustrate the systems with some

simulations and yield some more informal and practical insight into the behaviour of these

systems.

Place, publisher, year, edition, pages
2013. , 43 p.
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:kth:diva-129164OAI: oai:DiVA.org:kth-129164DiVA: diva2:650284
Supervisors
Available from: 2013-09-20 Created: 2013-09-20 Last updated: 2013-09-20Bibliographically approved

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Markus Himmelstrand, Victor Wilén kandidatex(1360 kB)515 downloads
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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
More languages
Output format
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