no. 3
Multiple brake orbits on compact convex symmetric reversible hypersurfaces in 𝐑 2n
Annales de l'I.H.P. Analyse non linéaire, Tome 31 (2014) no. 3, pp. 531-554

In this paper, we prove that there exist at least [n+1 2]+1 geometrically distinct brake orbits on every C 2 compact convex symmetric hypersurface Σ in 𝐑 2n for n⩾2 satisfying the reversible condition NΣ=Σ with N= diag (-I n ,I n ). As a consequence, we show that there exist at least [n+1 2]+1 geometrically distinct brake orbits in every bounded convex symmetric domain in 𝐑 n with n⩾2 which gives a positive answer to the Seifert conjecture of 1948 in the symmetric case for n=3. As an application, for n=4and5, 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.

DOI : 10.1016/j.anihpc.2013.03.010
Classification : 58E05, 70H05, 34C25
Keywords: Brake orbit, Maslov-type index, Seifert conjecture, Convex symmetric 
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     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
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Zhang, Duanzhi; Liu, Chungen. Multiple brake orbits on compact convex symmetric reversible hypersurfaces in $ {\mathbf{R}}^{2n}$. Annales de l'I.H.P. Analyse non linéaire, Tome 31 (2014) no. 3, pp. 531-554. doi: 10.1016/j.anihpc.2013.03.010

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