Index iteration theories for periodic orbits: Old and new

被引：5

作者：

Duan, Huagui ^{[1
,2
]}

Long, Yiming ^{[2
,3
]}

Zhu, Chaofeng ^{[2
,3
]}

机构：

[1] Nankai Univ, Sch Math Sci, Tianjin 300071, Peoples R China

[2] Nankai Univ, LPMC, Tianjin 300071, Peoples R China

[3] Nankai Univ, Chern Inst Math, Tianjin 300071, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2020年 / 201卷

关键词：

Hamiltonian systems; Index theories; Iteration theories; Periodic solutions; Multiplicity; Stability; MASLOV-TYPE INDEX; COMPACT CONVEX HYPERSURFACES; NONCONTRACTILE CLOSED GEODESICS; ELLIPTIC LAGRANGIAN SOLUTIONS; LINEAR HAMILTONIAN-SYSTEMS; EQUIVARIANT MORSE-THEORY; SYMPLECTIC PATHS; MINIMAL PERIOD; RELATIVE EQUILIBRIA; RESONANCE IDENTITY;

D O I：

10.1016/j.na.2020.111999

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we give a survey of the index iteration theories developed for periodic solution orbits of Hamiltonian systems in treating various problems from 1950s up to now, including some recent developments, and some of their applications to periodic solution problems. (C) 2020 Elsevier Ltd. All rights reserved.

引用

页数：26

共 156 条

[11] Bangert V., 1985, JAHRESBER DTSCH MATH, V87, P39
[12] BANGERT V., 1993, Internat. J. Math., V4, P1, DOI 10.1142/S0129167X93000029
[13] The existence of two closed geodesics on every Finsler 2-sphere
Bangert, Victor
Long, Yiming
[J]. MATHEMATISCHE ANNALEN, 2010, 346 (02) : 335 - 366
[14] A generalization of the Weinstein-Moser theorems on periodic orbits of a Hamiltonian system near an equilibrium
Bartsch, T
[J]. ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 1997, 14 (06): : 691 - 718
[15] Birkhoff G. D., 1927, Dynamical systems, V9
[16] Dynamical systems with two degrees of freedom
Birkhoff, George D.
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1917, 18 (1-4) : 199 - 300
[17] Booss-Bavnbek B, 2018, MEM AM MATH SOC, V252, pIX
[18] The Maslov index in weak symplectic functional analysis
Booss-Bavnbek, Bernhelm
Zhu, Chaofeng
[J]. ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 2013, 44 (03) : 283 - 318
[19] ON THE ITERATION OF CLOSED GEODESICS AND THE STURM INTERSECTION THEORY
BOTT, R
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1956, 9 (02) : 171 - 206
[20] Maslov index for homoclinic orbits of Hamiltonian systems
Chen, Chao-Nien
Hu, Xijun
[J]. ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2007, 24 (04): : 589 - 603

← 1 2 3 4 5 6 7 8 9 10 →