Iterated index formulae for closed geodesics with applications
By Chun-gen Liu, Y. Long. Science China Mathematics, 2002
51 citations recorded by the source corpus.
In this paper, various precise iteration equalities and inequalities of Morse indices for the closed geodesics are established. As applications of these formulae, multiplicity results of closed geodesics on some Riemannian manifolds are proved.
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Citations in the corpus
- Stability of closed geodesics on Finsler 2-spheres (2008, background): “[17], Chapter 12 of [20], also [1, 2,4]).”
- The Relation of the Morse Index of Closed Geodesics with the Maslov–type Index of Symplectic Paths (2005, methodology): “For the Maslov-type index theory, there are various iteration index formulae for(i(γ m ) ,ν (γ m )) of the iterated symplectic paths γ m . For this topic, refer to the references: [ 6 ,14,16], [17] and”
- Multiple closed geodesics on bumpy Finsler n-spheres (2007, background): “nsler Sn = (Sn,F). Lemma 6.1. Under the assumption (F), the mean index of the closed geodesic cmust satisfy ˆi(c) >0. Proof. If ˆi(c) = 0, then we have i(cm) = 0 for all m≥ 1 (cf. Corollary 4.2 of [LLo1]). By Theorem 3.1, we have bn−1 = 1. By Proposition 2.1,we have C0(E,cm) = Q, Cq(E,cm) = 0 for”
- Multiple closed geodesics on 3-spheres (2009, background): “Note that for a closed geodesic c on a Finsler manifold (M,F), by [25] in 2002 of C.”
- The existence of two closed geodesics on every Finsler 2-sphere (2007, methodology): “Lon1] (cf. [Lon3]), there are nine possible cases for the sequences {i(cm)}m≥1 and {ν(cm)}m≥1 depending on the different symplectic normal forms of the linearized Poincar´e map of c. Note that here by [LLo2] the iteration formulae in [Lon1] work for Morse indices of closed geodesics on Riemannian and”