MASLOV-TYPE INDEX THEORY FOR SYMPLECTIC PATHS AND SPECTRAL FLOW (Ⅰ) 被引量：7

MASLOV-TYPE INDEX THEORY FOR SYMPLECTIC PATHS AND SPECTRAL FLOW (Ⅰ)

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摘要 The spectral flow for paths of admissible operators in arbitrary Banach space is defined, and some properties of the spectral flow is studied. The spectral flow for paths of admissible operators in arbitrary Banach space is defined, and some properties of the spectral flow is studied.

作者 ZHUCHAOFENG LONGYIMING

机构地区 NvmkalInstituteofMathematics ProjectsupportedbytheNationalNaturalScienceFoundationofChina

出处《Chinese Annals of Mathematics,Series B》 SCIE CSCD 1999年第4期413-424,共12页 数学年刊（B辑英文版）

关键词马斯罗型指数函数相对论非自伴算子光谱流动 Relative Morse index, Non-selfadjoint operator, Spectral flow

分类号 O19 [理学—基础数学]

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1胡锡俊,龙以明.Closed characteristics on non-degenerate star-shaped hypersurfaces in R^(2n)[J].Science China Mathematics,2002,45(8):1038-1052. 被引量：4
2Hu XiJun,Sun ShanZhong.Morse index and the stability of closed geodesics[J].Science China Mathematics,2010,53(5):170-175. 被引量：5
3Fei Guihua,Qiu Qingjiu.PERIODIC SOLUTIONS OF ASYMPTOTICALLY LINEA RHAMILTONIAN SYSTEMS[J].Chinese Annals of Mathematics,Series B,1997,18(3):359-372. 被引量：7
4LONG YIMING .ON THE MINIMAL PERIOD FOR PERIODIC SOLUTION PROBLEM OF NONLINEAR HAMILTONIAN SYSTEMS[J].Chinese Annals of Mathematics,Series B,1997,18(4):481-484. 被引量：6
5ChunGenLIU.The Relation of the Morse Index of Closed Geodesics with the Maslov-type Index of Symplectic Paths[J].Acta Mathematica Sinica,English Series,2005,21(2):237-248. 被引量：6
6Chungen LIU.Maslov P-Index Theory for a Symplectic Path with Applications[J].Chinese Annals of Mathematics,Series B,2006,27(4):441-458. 被引量：6
7Yu Ming XIAO.Periodic Solutions with Prescribed Minimal Period for the Second Order Hamiltonian Systems with Even Potentials[J].Acta Mathematica Sinica,English Series,2010,26(5):825-830. 被引量：2
8龙以明.MASLOV-TYPE INDEX, DEGENERATE CRITICAL POINTS, AND ASYMPTOTICALLY LINEAR HAMILTONIAN SYSTEMS[J].Science China Mathematics,1990,33(12):1409-1419. 被引量：17
9Hui LIU.Stability of Symmetric Closed Characteristics on Symmetric Compact Convex Hypersurfaces in R^(2n) under a Pinching Condition[J].Acta Mathematica Sinica,English Series,2012,28(5):885-900. 被引量：3
10刘春根.次二次Hamilton系统的对偶Morse指标及其闭特征的稳定性[J].数学学报（中文版）,2001,44(6):1073-1088. 被引量：1

引证文献7

1张端智.Maslov型指标及非线性Hamilton系统中的闸轨道[J].中国科学（A辑）,2007,37(3):301-311.
2Chungen LIU,Qi WANG.Some Abstract Critical Point Theorems for Self-adjoint Operator Equations and Applications[J].Chinese Annals of Mathematics,Series B,2011,32(1):1-14.
3Guoyuan CHEN.Fredholm Index and Spectral Flow in Non-self-adjoint Case[J].Acta Mathematica Sinica,English Series,2013,29(5):975-992.
4ZHANG DuanZhi.Symmetric period solutions with prescribed minimal period for even autonomous semipositive Hamiltonian systems[J].Science China Mathematics,2014,57(1):81-96.
5Gao Sheng ZHU.Indices and Stability of the Lagrangian System on Riemannian Manifold[J].Acta Mathematica Sinica,English Series,2021,37(4):565-580.
6Xi Jun HU,Li WU.Mean Index for Non-periodic Orbits in Hamiltonian Systems[J].Acta Mathematica Sinica,English Series,2022,38(1):291-310.
7LI Jia-yang,WANG Qi.The Existence of Solutions for a Class of Schr¨odinger Equations via Morse Index Theory[J].Chinese Quarterly Journal of Mathematics,2022,37(3):274-280.

1LONG YIMING,ZHU CHAOFENG.MASLOV-TYPE INDEX THEORYFOR SYMPLECTIC PATHS AND SPECTRAL FLOW(II)[J].Chinese Annals of Mathematics,Series B,2000,21(1):89-108. 被引量：8
2Guoyuan CHEN.Fredholm Index and Spectral Flow in Non-self-adjoint Case[J].Acta Mathematica Sinica,English Series,2013,29(5):975-992.
3侯国林,阿拉坦仓.一类无穷维Hamilton算子的谱[J].内蒙古大学学报（自然科学版）,2007,38(3):247-251. 被引量：14
4黄俊杰,阿拉坦仓.上三角型无穷维Hamilton算子的连续谱[J].南京理工大学学报,2005,29(2):240-243. 被引量：7
5阿拉坦仓,黄俊杰.一类无穷维Hamilton算子的谱分布[J].大连理工大学学报,2004,44(3):326-329. 被引量：11
6黄俊杰,阿拉坦仓,范小英.无穷维Hamilton算子的谱结构[J].中国科学（A辑）,2008,38(1):71-78. 被引量：22
7王华,阿拉坦仓,黄俊杰.上三角无穷维Hamilton算子的剩余谱[J].数学的实践与认识,2010,40(3):195-201.
8Duan-zhi ZHANG School of Mathematical Sciences, Peking University, Beijing 100871, China.Maslov-type index and brake orbits in nonlinear Hamiltonian systems[J].Science China Mathematics,2007,50(6):761-772. 被引量：1
9马逸尘,胡常兵,刘之行.非自伴算子时间离散化惯性流形[J].数学进展,2000,29(1):36-50.
10范漪涵,孙长银.关于非自伴算子D^4+X~α+iX~β的极限点性质[J].三峡大学学报（人文社会科学版）,1998,21(3):11-16.

Chinese Annals of Mathematics,Series B

1999年第4期

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MASLOV-TYPE INDEX THEORY FOR SYMPLECTIC PATHS AND SPECTRAL FLOW (Ⅰ) 被引量：7

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