Homotopical rigidity of polygonal billiards

Result code in IS VaVaI

RIV/68407700:21110/14:00225936 - isvavai.cz

Result on the web

http://dx.doi.org/10.1016/j.topol.2014.06.003

DOI - Digital Object Identifier

10.1016/j.topol.2014.06.003

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_x - 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

Name of the periodical

Topology and Its Applications

ISSN

0166-8641

e-ISSN

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Volume of the periodical

173

Issue of the periodical within the volume

AUGust

Country of publishing house

NL - THE KINGDOM OF THE NETHERLANDS

Number of pages

17

Pages from-to

308-324

UT code for WoS article

000339983900025

EID of the result in the Scopus database

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