A symmetric property in the enhanced common index jump theorem with applications to the closed geodesic problem
type: Item
instance of: scholarly article
title: A symmetric property in the enhanced common index jump theorem with applications to the closed geodesic problem
zbMATH Open document ID: 1490.53058
author: Muhammad Hamid
author: Wei Wang
published in: Discrete and Continuous Dynamical Systems
publication date: 2022-02-28T00:00:00Z
review text: In the present paper, the authors prove a symmetric property for the indices of symplectic paths in the enhanced common index jump theorem. Further, they prove that every compact Finsler manifold \((M,F)\) with reversibility \(\lambda\) and flag curvature \(K\) satisfying \((\frac{\lambda}{\lambda+1})^2<K\leq 1\), there exist two elliptic closed geodesics whose linearized Poincaré map has an eigenvalue of the form \(e^{\sqrt{-1\theta}}\) with \(\frac{\theta}{\pi}\notin Q\) provided the number of closed geodesics on \(M\) is finite. All the work given by them is useful in development of the differential geometry.
reviewed by: V. K. Chaubey
Mathematics Subject Classification ID: 53C22
Mathematics Subject Classification ID: 53C60
Mathematics Subject Classification ID: 58E10
zbMATH DE Number: 7481826
zbMATH Keywords: Finsler manifold
zbMATH Keywords: closed geodesic
zbMATH Keywords: index iteration
zbMATH Keywords: Morse theory
MaRDI profile type: Publication
full work available at URL: dcds.2021178
OpenAlex ID: W3217244092
cites work: The existence of two closed geodesics on every Finsler 2-sphere
cites work: Two elliptic closed geodesics on positively curved Finsler spheres
cites work: Multiple closed geodesics on bumpy Finsler \(n\)-spheres
cites work: The index growth and multiplicity of closed geodesics
cites work: Two closed geodesics on compact simply connected bumpy Finsler manifolds
cites work: The enhanced common index jump theorem for symplectic paths and non-hyperbolic closed geodesics on Finsler manifolds
cites work: The optimal lower bound estimation of the number of closed geodesics on Finsler compact space form \(S^{2n+1}/ \Gamma \)
cites work: Iterated index formulae for closed geodesics with applications.
cites work: Bott formula of the Maslov-type index theory
cites work: Precise iteration formulae of the Maslov-type index theory and ellipticity of closed characteristics
cites work: Index theory for symplectic paths with applications
cites work: Multiple closed geodesics on 3-spheres
cites work: Stability of closed geodesics on Finsler 2-spheres
cites work: Closed characteristics on compact convex hypersurfaces in \(\mathbb{R}^{2n}\)
cites work: A sphere theorem for non-reversible Finsler metrics
cites work: Existence of closed geodesics on positively curved Finsler manifolds
cites work: The second closed geodesic on Finsler spheres of dimension 𝑛>2
cites work: Lectures on Finsler geometry
cites work: Closed geodesics on positively curved Finsler spheres
cites work: On a conjecture of Anosov
cites work: On the average indices of closed geodesics on positively curved Finsler spheres
cites work: Multiple closed geodesics on positively curved Finsler manifolds
cites work: Geometry of the Katok examples
DOI: 10.3934/DCDS.2021178
description: scientific article; zbMATH DE number 7481826