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On Moser’s boundedness problem of dual Billiards

  • LONG LI (a1)
Abstract
Abstract

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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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[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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