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Three rods on a ring and the triangular billiard

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Abstract

We demonstrate the equoivalence of two seemingly disparate dynamical systems. One consits of three hard rods sliding along a frictionless ring and making elastic collisions. The other consists of one ball moving on a frictionless triangular table with elastic rails. Several applications of this result are discussed.

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References

  1. L. Onsager, Unpublished lectures, Yale University (1965); Ya. G. Sinai,Introduction to Ergodic Theory (Princeton University Press, Princeton, New Jersey, 1976).

  2. S. Tabachnikov, Billiards: Panoramas and syntheses,Soc. Math. France (1995)

  3. E. Gutkin, Biliards in polygons: Survey of recent results,J. Stat. Phys. 81:7 (1996).

    Google Scholar 

  4. G. Galperin, T. Krüger, and S. Troubetskoy, Local instability of orbits in polygonal and polyhedral billiards,Commun. Math. Phys. 169:463 (1995).

    Google Scholar 

  5. S. L. Glashow and L. Mittag,The Physics of Billiards. in preparation.

  6. H. Masur, Closed trajectories for quadratic differentials with an application to billiards,Duke Math. J. 53:307 (1986); M. Boshernitzan, G. Galperin, T. Krüger, and S. Trobetsckoy, Periodic billiard orbits are dense in rational polygons, preprint (1996).

    Google Scholar 

  7. S. Kerckhoff, H. Masur, and J. Smille, Ergodicity of biliard flows and quadratic differentials,Ann. Math. 124:293 (1986).

    Google Scholar 

  8. C. Boldrighini, M. Keane, and F. Marchetti, Billiards in polygons.,Ann. Prob. 6:532 (1978).

    Google Scholar 

  9. L. Tonks, The complete equation of state of one, two, and three dimensional gases of hard spheres,Phys. Rer. 50:955 (1936) see also D. W. Jepson, Dynamics of a simple manybody system of hard rods,J. Math. Phys. 6:405 (1965).

    Google Scholar 

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Glashow, S.L., Mittag, L. Three rods on a ring and the triangular billiard. J Stat Phys 87, 937–941 (1997). https://doi.org/10.1007/BF02181254

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  • DOI: https://doi.org/10.1007/BF02181254

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