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Asymptotic periodicity in outer billiards with contraction

Published online by Cambridge University Press:  14 June 2018

JOSÉ PEDRO GAIVÃO*
Affiliation:
Departamento de Matemática e CEMAPRE, ISEG, Universidade de Lisboa, Rua do Quelhas 6, 1200-781 Lisboa, Portugal email jpgaivao@iseg.utl.pt

Abstract

We show that for almost every $(P,\unicode[STIX]{x1D706})$, where $P$ is a convex polygon and $\unicode[STIX]{x1D706}\in (0,1)$, the corresponding outer billiard about $P$ with contraction $\unicode[STIX]{x1D706}$ is asymptotically periodic, i.e., has a finite number of periodic orbits and every orbit is attracted to one of them.

Type
Original Article
Copyright
© Cambridge University Press, 2018 

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