The optimal lower bound estimation of the number of closed geodesics on Finsler compact space form $$S^{2n+1}/ \Gamma $$

Liu, Hui

doi:10.1007/s00526-019-1567-3

Cited by 5 publications

(2 citation statements)

References 47 publications

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“…Furthermore, Liu, Long and Xiao [25] established the resonance identity for noncontractible closed geodesics of class [h] on compact space form M = S n /Γ and obtained at least two non-contractible closed geodesics of class [h] provided Γ is abelian and h is nontrivial in π 1 (M ). Recently, Liu [27] obtained an optimal lower bound estimation of the number of contractible closed geodesics on bumpy Finsler compact space form S 2n+1 /Γ with reversibility λ and flag curvature K satisfying…”

Section: Introductionmentioning

confidence: 99%

Multiplicity of non-contractible closed geodesics on Finsler compact space forms

Liu¹,

Wang²

2022

Preprint

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Section: Introductionmentioning

confidence: 99%

Multiplicity of non-contractible closed geodesics on Finsler compact space forms

Liu¹,

Wang²

2022

Preprint

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“…For the existence of closed geodesics on Finsler manifolds, we refer the readers to [1], [14], [18], [19], [3], [4], [21], [22], [23], [5], [6] and [9]. For the stability of closed geodesics, in [15], Y.…”

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confidence: 99%

A symmetric property in the enhanced common index jump theorem with applications to the closed geodesic problem

Hamid

Wang

2022

DCDS

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<p style='text-indent:20px;'>In this paper, we prove a symmetric property for the indices for symplectic paths in the enhanced common index jump theorem (cf. Theorem 3.5 in [<xref ref-type="bibr" rid="b6">6</xref>]). As an application of this property, we prove that on every compact Finsler manifold <inline-formula><tex-math id="M1">\begin{document}$ (M, \, F) $\end{document}</tex-math></inline-formula> with reversibility <inline-formula><tex-math id="M2">\begin{document}$ \lambda $\end{document}</tex-math></inline-formula> and flag curvature <inline-formula><tex-math id="M3">\begin{document}$ K $\end{document}</tex-math></inline-formula> satisfying <inline-formula><tex-math id="M4">\begin{document}$ \left(\frac{\lambda}{\lambda+1}\right)^2<K\le 1 $\end{document}</tex-math></inline-formula>, there exist two elliptic closed geodesics whose linearized Poincaré map has an eigenvalue of the form <inline-formula><tex-math id="M5">\begin{document}$ e^{\sqrt {-1}\theta} $\end{document}</tex-math></inline-formula> with <inline-formula><tex-math id="M6">\begin{document}$ \frac{\theta}{\pi}\notin{\bf Q} $\end{document}</tex-math></inline-formula> provided the number of closed geodesics on <inline-formula><tex-math id="M7">\begin{document}$ M $\end{document}</tex-math></inline-formula> is finite.</p>

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Multiplicity of non-contractible closed geodesics on Finsler compact space forms

Liu

Wang

2022

Calc. Var.

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The optimal lower bound estimation of the number of closed geodesics on Finsler compact space form $$S^{2n+1}/ \Gamma $$

Cited by 5 publications

References 47 publications

Multiplicity of non-contractible closed geodesics on Finsler compact space forms

Multiplicity of non-contractible closed geodesics on Finsler compact space forms

A symmetric property in the enhanced common index jump theorem with applications to the closed geodesic problem

Multiplicity of non-contractible closed geodesics on Finsler compact space forms

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