Advanced Search
Article Contents
Article Contents

Maximizing orbits for higher-dimensional convex billiards

Abstract Related Papers Cited by
  • The main result of this paper is that, in contrast to the 2D case, for convex billiards in higher dimensions, for every point on the boundary, and for every $n$, there always exist billiard trajectories developing conjugate points at the $n$-th collision with the boundary. We shall explain that this is a consequence of the following variational property of the billiard orbits in higher dimension. If a segment of an orbit is locally maximizing, then it can not pass too close to the boundary. This fact follows from the second variation formula for the length functional. It turns out that this formula behaves differently with respect to "longitudinal'' and "transverse'' variations.
    Mathematics Subject Classification: Primary: 37J50; Secondary: 37J35.


    \begin{equation} \\ \end{equation}
  • 加载中

Article Metrics

HTML views() PDF downloads(73) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint