Index Theory for Symplectic Paths with Applications

By Y. Long. 2002

517 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/7091704c33479a788207c386ca77dc9e7228c5f4

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In Mathematical Physics

Citations in the corpus

Seifert Conjecture in the Even Convex Case (2013, methodology): “12 of [21]) Splitting number S± M (ω) are well defined, i.”
Maslov-Type Index Theory For Symplectic Paths With Lagrangian Boundary Conditions (2007, methodology): “¥ The following result was proved in [16].”
Continuity in weak topology: higher order linear systems of ODE (2008, background): “It can be generalized to linear Hamiltonian systems of higher degrees of freedom [ 22 ] , and even to positively homogeneous planar systems with almost periodic coefficients [21] . The rotation number”
Stability of closed geodesics on Finsler 2-spheres (2008, background): “Chapter 8 of [20]) work for Morse indices of iterated closed geodesics (cf.”
Lusternik–Schnirelmann theory and closed Reeb orbits (2016, background): “eory 4.1. Preliminaries: deﬁnitions and basic facts. In this section we recall for the reader’s convenience some basic properties of the mean and Conley–Zehnder indices. We refer the reader to, e.g., [Lo02] or [SZ, Sect. 3] for a more thorough treatment; see also [Ab, Gut14] and, for a very quick in”
Index theory for linear selfadjoint operator equations and nontrivial solutions for asymptotically linear operator equations (2007, unknown): “…Φ′′V (x0)||V = sup ||u||V ≤1,||v||V ≤1 | ∫ 1 0 ((H ′′(t, x(t)) −H ′′(t, x0(t)))u(t), v(t))dt| ≤ n∑ i,j=−n | ∫ 1 0 ((H ′′(t, x(t))−H ′′(t, x0(t)))ej(t), ei(t))dt| + 4M( 1 |λ−n−1| + 1 |λn+1| ) Because λj → ±∞ as j → ±∞ and from Theorem 4 in page 97 of Ekeland’s book[13] it follows that for fixed…”
The enhanced common index jump theorem for symplectic paths and non-hyperbolic closed geodesics on Finsler manifolds (2015, methodology): “ik. For every 2P ˝(2n) f 2C([0;˝];Sp(2n)) j (0) = I 2ng, we extend (t) to t2[0;m˝] for every m2N by m(t) = (t j˝) (˝)j 8j˝t(j+ 1)˝ 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 m by (i( ;m);( ;m)). By [Liu] and [LLo], the Morse indices ”
Multiple closed geodesics on 3-spheres (2009, methodology): “7 of [29]) for any γ ∈ Pτ (2d) with d ∈ N, we obtain”
The Relation of the Morse Index of Closed Geodesics with the Maslov–type Index of Symplectic Paths (2005, methodology): “By the definition of the Maslov-type index of symplectic paths [13, 14, 19 ] and Corollary 3.5, there hold”
Loop Products and Closed Geodesics (2007, methodology): “We have the following theorems of Morse and Bott [Mo1], [Bo2], [Mi], [Bo1], [L], [K] Cor.”
Maslov index for homoclinic orbits of hamiltonian systems (2007, background): “This is so called relative Morse index of which many interesting properties and applications have been obtained [2,11,20,27] for periodic orbits of Hamiltonian systems.”
Multiple brake orbits in bounded convex symmetric domains (2006, result): “Because the discussion is similar to that of [29], we omit certain details here.”