Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

Billiards in Polygons

Carlo Boldrighini, Michael Keane and Federico Marchetti
The Annals of Probability
Vol. 6, No. 4 (Aug., 1978), pp. 532-540
Stable URL: http://www.jstor.org/stable/2243120
Page Count: 9
  • Read Online (Free)
  • Download ($19.00)
  • Subscribe ($19.50)
  • Cite this Item
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Billiards in Polygons
Preview not available

Abstract

Some questions concerning the orbits of a billiard ball in a polygon are studied. It is shown that almost all such orbits come arbitrarily close to a vertex of the polygon, implying that the entropy of the corresponding geodesic flow is zero. For polygons with rational angles, we show by using interval exchange transformations that almost all orbits are spatially dense. Two applications are given.

Page Thumbnails

  • Thumbnail: Page 
532
    532
  • Thumbnail: Page 
533
    533
  • Thumbnail: Page 
534
    534
  • Thumbnail: Page 
535
    535
  • Thumbnail: Page 
536
    536
  • Thumbnail: Page 
537
    537
  • Thumbnail: Page 
538
    538
  • Thumbnail: Page 
539
    539
  • Thumbnail: Page 
540
    540