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Abstract
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We study
-geodesics,
those closed geodesics that minimize on any subinterval of length
,
where
is the length of the geodesic. We investigate the existence and behavior of
these curves on doubled polygons and show that every doubled regular
-gon admits a
-geodesic. For the doubled
regular
-gons, with
an odd prime, we conjecture
that
is the minimum
value for
such that the
space admits a
-geodesic.
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Keywords
closed geodesics, regular polygons, billiard paths
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Mathematical Subject Classification 2010
Primary: 53C20, 53C22
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Milestones
Received: 24 January 2019
Revised: 7 February 2019
Accepted: 18 February 2019
Published: 12 October 2019
Communicated by Frank Morgan
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