The Relation of the Morse Index of Closed Geodesics with the Maslov–type Index of Symplectic Paths

73 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Stability of closed geodesics on Finsler 2-spheres (2008, unknown): “1 of [16] of C.”
Progress in research on Chinese urbanization (2012, background): “The development of the tertiary industry, such as the development of tourism (Lu et al., 2006; Zhou and Yu, 2004; Zhou and Liu, 2005) promoted the rapid urbanization (Liu, 2000; Chen et al, 2004; Lu and Chen, 2005) and improved quality of Chinese urbanization (Du, 2005).”
Maslov-Type Index Theory For Symplectic Paths With Lagrangian Boundary Conditions (2007, background): “If c is a closed geodesic on a Riemannian manifold M , we know from [15] that ind(c) = i1(c).”
The enhanced common index jump theorem for symplectic paths and non-hyperbolic closed geodesics on Finsler manifolds (2015, unknown): “τ] for every m ∈ N by γm(t) = γ(t −jτ)γ(τ)j ∀ jτ ≤ t ≤ (j +1)τ and j = 0,1,...,m−1, (3.9) as in P.114 of [Lon1]. As in [LoZ] and [Lon3], we denote the Maslov-type indices of γm by (i(γ,m),ν(γ,m)). By [Liu] and [LLo], the Morse indices of an oriented closed geodesic c coincide to the Maslov-type indi”