On the minimal number of periodic orbits on some hypersurfaces in ℝ²ⁿ

2015/08/01 by Jean Gutt, Jungsoo Kang, Gutt, Jean +1
Mathematics · #Algebraic Geometry and Number Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Symplectic Geometry (math.SG) #math.DS #math.SG

paper · pdf · doi:10.48550/arxiv.1508.00166

To appear in Annales de l'Institut Fourier

openalex publication_date 2015/08/01 · arxiv created 2016/04/22 · arxiv updated 2016/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study periodic orbits on a nondegenerate dynamically convex starshaped hypersurface in ℝ²ⁿ along the lines of Long and Zhu, but using properties of the S¹-equivariant symplectic homology. We prove that there exist at least n distinct simple periodic orbits on any nondegenerate starshaped hypersurface in ℝ²ⁿ satisfying the condition that the minimal Conley-Zehnder index is at least n-1. The condition is weaker than dynamical convexity.

Citations

• Morse‐type index theory for flows and periodic solutions for Hamiltonian Equations

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