2025/06/05 by Wei Wang, Wang, Wei · 1 voice
Mathematics · #34C25 #37J46 #58E05 #FOS: Mathematics #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions #Symplectic Geometry (math.SG) #math.SG
paper · pdf · doi:10.48550/arxiv.2506.04546
openalex publication_date 2025/06/05 · arxiv published 2025/06/05 · arxiv updated 2025/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we prove that for every dynamically convex compact star-shaped hypersurface Σ⊂ℝ2n, there exist at least \lfloor(n+1)/(2)\rfloor geometrically distinct closed characteristics possessing irrational mean indices provided the number of geometrically distinct closed characteristics on Σ is finite, this improves Theorem 1.3 in \citeLoZ of Y. Long and C. Zhu by finding one more closed characteristic possessing irrational mean index when n is odd. Moreover, there exist at least \lfloor(n+1)/(2)\rfloor+1 geometrically distinct closed characteristics such that the ratio of the mean indices of any two of them is a irrational number provided the number of geometrically distinct closed characteristics on Σ is finite, this improves Theorem 1.2 in \citeHuO of X. Hu and Y. Ou when n is odd. In particular, these estimates are sharp for n=3.