Multiple brake orbits on compact convex symmetric reversible hypersurfaces in

  • Duanzhi Zhang

    School of Mathematics and LPMC, Nankai University, Tianjin 300071, People's Republic of China
  • Chungen Liu

    School of Mathematics and LPMC, Nankai University, Tianjin 300071, People's Republic of China

Abstract

In this paper, we prove that there exist at least geometrically distinct brake orbits on every compact convex symmetric hypersurface Σ in for satisfying the reversible condition with . As a consequence, we show that there exist at least geometrically distinct brake orbits in every bounded convex symmetric domain in with which gives a positive answer to the Seifert conjecture of 1948 in the symmetric case for . As an application, for , we prove that if there are exactly n geometrically distinct closed characteristics on Σ, then all of them are symmetric brake orbits after suitable time translation.

Cite this article

Duanzhi Zhang, Chungen Liu, Multiple brake orbits on compact convex symmetric reversible hypersurfaces in . Ann. Inst. H. Poincaré Anal. Non Linéaire 31 (2014), no. 3, pp. 531–554

DOI 10.1016/J.ANIHPC.2013.03.010