Existence of closed characteristics on compact convex hypersurfaces in $\R^{2n}

Details Existence of closed characteristics on compact convex hypersurfaces in $\R^{2n} Existence of closed characteristics on compact convex hypersurfaces in $\R^{2n}

2011-12-23

arxiv.org/abs/1112.5501v3

Mathematics

Symplectic Geometry

25 pages. arXiv admin note: substantial text overlap with arXiv:math/0701673

Scientific paper

In this paper, we prove there exist at least $[\frac{n+1}{2}]+1$ geometrically distinct closed characteristics on every compact convex hypersurface $\Sg$ in $\R^{2n}$. Moreover, there exist at least $[\frac{n}{2}]+1$ geometrically distinct non-hyperbolic closed characteristics on $\Sg$ in $\R^{2n}$ provided the number of geometrically distinct closed characteristics on $\Sg$ is finite.

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