Homotopical rigidity of polygonal billiards

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21110%2F14%3A00225936" target="_blank" >RIV/68407700:21110/14:00225936 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.topol.2014.06.003" target="_blank" >http://dx.doi.org/10.1016/j.topol.2014.06.003</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.topol.2014.06.003" target="_blank" >10.1016/j.topol.2014.06.003</a>

Result language
angličtina
Original language name
Homotopical rigidity of polygonal billiards
Original language description
Consider two k-gons P and Q. We say that the billiard flows in P and Q are homotopically equivalent if the set of conjugacy classes in the fundamental group of P, viewed as a punctured sphere, which contain a periodic billiard orbit agrees with the analogous set for Q. We study this equivalence relationship and compare it to the notions of order equivalence and code equivalence, introduced in [1,2]. In particular we show if P is a rational polygon, and Q is homotopically equivalent to P, then P and Q are similar, or affinely similar if all sides of P are vertical and horizontal.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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