Closed characteristics on compact convex hypersurfaces in ${\mathbb{R}}^8$

Abstract

In this paper, we prove there exist at least four geometrically distinct closed characteristics on every compact convex hypersurface $\Sg$ in ${\mathbb{R}}^8$. This gives a confirmed answer in the case $n=4$ to a long standing conjecture in Hamiltonian analysis since the time of A. M. Liapounov in 1892 (cf. P. 235 of \cite{Eke3}).

62 pages. Some details are added and some typos are corrected in this version. arXiv admin note: substantial text overlap with arXiv:1112.5501, arXiv:math/0701673, arXiv:math/0701608

References in corpus (1)

• Index iteration theory for symplectic paths with applications to nonlinear Hamiltonian systems

Cited by in corpus (3)

• On the minimal number of periodic orbits on some hypersurfaces in ${\mathbb{R}}^{2n}$
• Non-hyperbolic closed characteristics on non-degenerate star-shaped hypersurfaces in ${\mathbf{R}}^{2n}$
• Multiplicity and ellipticity of closed characteristics on compact star-shaped hypersurfaces in ${\mathbf{R}}^{2n}$