A Non-varying Phenomenon with an Application to the Wind-Tree Model
2018 ◽
Vol 2020
(18)
◽
pp. 5642-5660
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Abstract We exhibit a non-varying phenomenon for the counting problem of cylinders, weighted by their area, passing through two marked (regular) Weierstrass points of a translation surface in a hyperelliptic connected component $\mathcal{H}^{hyp}(2g-2)$ or $\mathcal{H}^{hyp}(g-1,g-1)$, $g> 1$. As an application, we obtain the non-varying phenomenon for the counting problem of (weighted) periodic trajectories on the Ehrenfest wind-tree model, a billiard in the plane endowed with $\mathbb{Z}^2$-periodically located identical rectangular obstacles.
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2015 ◽
Vol 10
(10)
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pp. 995
◽
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2010 ◽
Vol 30
(6)
◽
pp. 1616-1618
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2009 ◽
Vol 28
(12)
◽
pp. 3150-3153
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1992 ◽
Vol 26
(5-6)
◽
pp. 1411-1420
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2018 ◽
Vol 74
(2)
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pp. I_427-I_432
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