On the minimal number of periodic orbits on some hypersurfaces in ${\mathbb{R}}^{2n}$

Abstract

We study periodic orbits on a nondegenerate dynamically convex starshaped hypersurface in ${\mathbb{R}}^{2n}$ along the lines of Long and Zhu, but using properties of the $S^1$-equivariant symplectic homology. We prove that there exist at least $n$ distinct simple periodic orbits on any nondegenerate starshaped hypersurface in ${\mathbb{R}}^{2n}$ satisfying the condition that the minimal Conley-Zehnder index is at least $n-1$. The condition is weaker than dynamical convexity.

To appear in Annales de l'Institut Fourier

References in corpus (2)

• Functors and Computations in Floer homology with Applications Part II
• The existence of two closed characteristics on every compact star-shaped hypersurface in ${\mathbf{R}}^4$

Cited by in corpus (4)

• Periodic Reeb orbits on prequantization bundles
• The enhanced common index jump theorem for symplectic paths and non-hyperbolic closed geodesics on Finsler manifolds
• 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 ${\mathbf{R}}^{2n}$