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  • Cited by 2
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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Bedaride, Nicolas 2012. A characterization of quasi-rational polygons. Nonlinearity, Vol. 25, Issue. 11, p. 3099.

    Schwartz, Richard 2011. Outer billiards on the Penrose kite: Compactification and renormalization. Journal of Modern Dynamics, Vol. 5, Issue. 3, p. 473.


On Moser’s boundedness problem of dual Billiards

  • LONG LI (a1)
  • DOI:
  • Published online: 01 April 2009

In this paper, the boundedness of the dual billiard orbits of trapezoids is obtained. This gives an example showing that there are also polygons, which are neither rational nor quasi-rational, with all of their dual billiard orbits bounded. Moreover, most of the orbits are Poisson-stable, which means that most points will come sufficiently near to their original positions under iterations of the dual billiard map.

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[1]J. Moser . Is the Solar System stable? Math. Intelligencer 1 (1978), 6571.

[2]F. Vivaldi and A. V. Shaidenko . Global stability of a class of discontinous dual billiards. Comm. Math. Phys. 110 (1987), 625640.

[4]E. Gutkin and N. Simanyi . Dual polygonal billiards and necklace dynamics. Comm. Math. Phys. 143 (1992), 431449.

[5]S. Tabachnikov . On the dual billiard problem. Adv. Math. 115 (1995), 221249.

[10]R. Schwartz . Unbounded orbits for outer billiards. I. J. Mod. Dyn. 1 (2007), 371424.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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