Precise Iteration Formulae of the Maslov-type Index Theory and Ellipticity of Closed Characteristics

By Y. Long. 2000

165 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/8f48a353eb29202628b51e97e644522ac78f5357

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In Computational Theory and Mathematics

1. Wei Wang
2. V. Bangert
3. Chun-gen Liu
4. Y. Long
5. Huagui Duan
6. Chaofeng Zhu
7. Xijun Hu
8. William D. Banks

In Mathematical Physics

1. Chun-gen Liu
2. Huagui Duan
3. Wei Wang
4. V. Bangert
5. Xijun Hu
6. Shanzhong Sun
7. Chaofeng Zhu
8. William D. Banks

In Statistical and Nonlinear Physics

1. Wei Wang
2. V. Bangert
3. Chun-gen Liu
4. Huagui Duan
5. Chaofeng Zhu
6. Xijun Hu
7. Shanzhong Sun
8. William D. Banks

Citations in the corpus

• Prime numbers with Beatty sequences (2007, background): “In the special case that (a, q) = (0, 1) or (1, 2) (the latter case corresponding to primes in the Long conjecture), we can use a well known bound on the error term in the Prime Number Theorem (proved independently by Korobov [13] and Vinogradov [25]) to achieve the following sharper result: Corolla”
• The enhanced common index jump theorem for symplectic paths and non-hyperbolic closed geodesics on Finsler manifolds (2015, unknown): “] of 1999, Y. Long established the basic normal form decomposition of symplectic matrices. Based on this result he further established the precise iteration formulae of indices of symplectic paths in [Lon2] of 2000. As in [Lon2], denote by N1(λ,b) = λ b 0 λ ! , for λ = ±1, b ∈ R, (3.1) D(λ) = λ 0 0 ”
• The Relation of the Morse Index of Closed Geodesics with the Maslov–type Index of Symplectic Paths (2005, background): “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”
• The existence of two closed geodesics on every Finsler 2-sphere (2007, methodology): “ν(cm) = nullity(D2E(cm)) − 1. As proved in [ Lon1 ] (cf.”
• Multiple brake orbits in bounded convex symmetric domains (2006, unknown): “7 of [28], or Corollary 8.”
• Multiple closed geodesics on 3-spheres (2009, background): “Chapter 12 of [29]), the index iteration formulae in [26] and [27] (cf.”
• Index and Stability of Symmetric Periodic Orbits in Hamiltonian Systems with Application to Figure-Eight Orbit (2009, background): “For the compact convex hypersurface in R 4 , a spectacular theorem of Hofer, Wysocki and Zehnder [HWZ] says that the number of geometrically different closed characteristics is either 2 or infinity, and Long [ L2 ] further proves that all the closed characteristics are elliptic if the number is fini”
• Stability of closed geodesics on Finsler 2-spheres (2008, methodology): “Long proved in [19], existence theorems of N.”
• Multiplicity of closed characteristics on symmetric convex hypersurfaces in $\mathbb{R}^{2n}$ (2001, background): “The details of the definitions and properties of these index and their iteration theories can be found in the above mentioned works as well as [16] and [17].”