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

Abstract

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 ${\mathbb{R}}^{2n}$. Moreover, there exist at least $[\frac{n}{2}]+1$ geometrically distinct non-hyperbolic closed characteristics on $\Sg$ in ${\mathbb{R}}^{2n}$ provided the number of geometrically distinct closed characteristics on $\Sg$ is finite.

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

References in corpus (1)

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

Cited by in corpus (8)

• The existence of two closed characteristics on every compact star-shaped hypersurface in ${\mathbf{R}}^4$
• Resonance Identities for Closed Characteristics on Compact Star-shaped Hypersurfaces in ${\mathbf{R}}^{2n}$
• Multiplicity of Closed Reeb Orbits on Prequantization Bundles
• Non-hyperbolic closed characteristics on non-degenerate star-shaped hypersurfaces in ${\mathbf{R}}^{2n}$
• Equivariant symplectic homology and multiple closed Reeb orbits
• Resonance identities and stability of symmetric closed characteristics on symmetric compact star-shaped hypersurfaces
• Perfect Reeb flows and action-index relations
• Multiplicity and ellipticity of closed characteristics on compact star-shaped hypersurfaces in ${\mathbf{R}}^{2n}$