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Journal Articles Topology and its Applications Year : 2014

Homotopical rigidity of polygonal billiards

Jozef Bobok
• Function : Author
Serge Troubetzkoy

Abstract

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 $P$ which contain a periodic billiard orbit agrees with the analogous set for $Q$. We study this equivalence relationship and compare it to the equivalence relations, order equivalence and code equivalence, introduced in \cite{BT1,BT2}. 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.

Dates and versions

hal-00700476 , version 1 (23-05-2012)

Identifiers

• HAL Id : hal-00700476 , version 1
• ARXIV :
• DOI :

Cite

Jozef Bobok, Serge Troubetzkoy. Homotopical rigidity of polygonal billiards. Topology and its Applications, 2014, 173, pp.308-324. ⟨10.1016/j.topol.2014.06.003⟩. ⟨hal-00700476⟩

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