Long Yiming | Academic Influence

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Long Yiming

Mathematics

#4693

World Rank

#6646

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Group Theory

#207

World Rank

#244

Historical Rank

Number Theory

#322

World Rank

#401

Historical Rank

Algebra

#527

World Rank

#698

Historical Rank

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Mathematics

Long Yiming's Degrees

Bachelors Mathematics Peking University
Masters Mathematics Peking University
PhD Mathematics Peking University

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Why Is Long Yiming Influential?

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According to Wikipedia, Long Yiming is a Chinese researcher, mathematician, and professor at Nankai University. He is a fellow of the Chinese Academy of Sciences. His research focuses on symplectic geometry, nonlinear functional analysis, celestial mechanics, the variation method, and the Hamiltonian system.

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Long Yiming's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Index Theory for Symplectic Paths with Applications (2002) (461)
Closed characteristics on compact convex hypersurfaces in $\R^{2n}$ (2001) (186)
Bott formula of the Maslov-type index theory (1999) (173)
MASLOV-TYPE INDEX, DEGENERATE CRITICAL POINTS, AND ASYMPTOTICALLY LINEAR HAMILTONIAN SYSTEMS (1990) (161)
Precise Iteration Formulae of the Maslov-type Index Theory and Ellipticity of Closed Characteristics (2000) (147)
The existence of two closed geodesics on every Finsler 2-sphere (2007) (111)
Multiple brake orbits in bounded convex symmetric domains (2006) (94)
Maslov-Type Index Theory for Symplectic Paths and Spectral Flow (II) (1980) (88)
Resonance identity, stability, and multiplicity of closed characteristics on compact convex hypersurfaces (2007) (84)
Nonlinear oscillations for classical Hamiltonian systems with bi-even subquadratic potentials (1995) (82)
Multiplicity of closed characteristics on symmetric convex hypersurfaces in $\mathbb{R}^{2n}$ (2001) (76)
A Maslov-type index theory for symplectic paths (1997) (75)
Multiple solutions of perturbed superquadratic second order Hamiltonian systems (1989) (71)
Four-Body Central Configurations¶with some Equal Masses (2002) (68)
The iteration formula of the Maslov-type index theory with applications to nonlinear Hamiltonian systems (1997) (65)
Multiple closed geodesics on 3-spheres (2009) (57)
Multiple closed geodesics on bumpy Finsler n-spheres (2007) (52)
Stability of closed geodesics on Finsler 2-spheres (2008) (52)
The Minimal Period Problem of Periodic Solutions for Autonomous Superquadratic Second Order Hamiltonian Systems (1994) (52)
Iterated index formulae for closed geodesics with applications (2002) (47)
Iteration Inequalities of the Maslov-Type Index Theory with Applications (2000) (46)
The index growth and multiplicity of closed geodesics (2010) (44)
Hyperbolic Closed Characteristics on Compact Convex Smooth Hypersurfaces inR2n (1998) (42)
The enhanced common index jump theorem for symplectic paths and non-hyperbolic closed geodesics on Finsler manifolds (2015) (40)
Linear Stability of Elliptic Lagrangian Solutions of the Planar Three-Body Problem via Index Theory (2012) (38)
Closed characteristics on partially symmetric compact convex hypersurfaces in R2n (2004) (36)
A note on the existence of multiple brake orbits (1993) (36)
The minimal period problem of classical Hamiltonian systems with even potentials (1993) (36)
THE STRUCTURE OF THE SINGULAR SYMPLECTIC MATRIX SET (1991) (35)
Multiple periodic points of the Poincaré map of Lagrangian systems on tori (2000) (35)
Two closed geodesics on compact simply connected bumpy Finsler manifolds (2016) (33)
Indexing domains of instability for Hamiltonian systems (1998) (31)
The existence of two closed characteristics on every compact star-shaped hypersurface in ℝ4 (2013) (31)
Geometric Characterizations for Variational Minimization Solutions of the 3-Body Problem (2000) (30)
Periodic solutions of perturbed superquadratic hamiltonian systems (1987) (29)
Closed characteristics on non-degenerate star-shaped hypersurfaces in R2n (2002) (28)
Periodic solutions for a class of nonautonomous Hamiltonian systems (2000) (28)
Multiplicity and stability of closed geodesics on bumpy Finsler 3-spheres (2006) (26)
Closed characteristics on compact convex hypersurfaces in R 2 n By (2004) (25)
Resonance Identities for Closed Characteristics on Compact Star-shaped Hypersurfaces in ${\bf R}^{2n}$ (2013) (21)
Multiple closed geodesics on Riemannian 3-spheres (2007) (21)
Maslov-Type Indices and Linear Stability of Elliptic Euler Solutions of the Three-Body Problem (2015) (20)
Topological structure of non-contractible loop space and closed geodesics on real projective spaces with odd dimensions (2015) (19)
Periodic solutions of superquadratic Hamiltonian systems with bounded forcing terms (1990) (19)
An optimal increasing estimate of the iterated Maslov-type indices (1998) (18)
Admissible Shapes of 4-Body Non-collinear Relative Equilibria (2003) (17)
A new class of problems in the calculus of variations (2013) (17)
Hyperbolic characteristics on star-shaped hypersurfaces (1999) (17)
Topological structures ofθ-subsets in symplectic groups (1999) (16)
Stable closed characteristics on partially symmetric convex hypersurfaces (2004) (15)
On the index theories for second order Hamiltonian systems 1 1 Partially supported by the NNSF of Ch (1998) (15)
Index Iteration Theory for Symplectic Paths with Applications to Nonlinear Hamiltonian Systems (2003) (15)
Closed characteristics on convex hypersurfaces (2002) (15)
Forced Oscillations for the Triple Pendulum (1990) (14)
The reduction of the linear stability of elliptic Euler–Moulton solutions of the n-body problem to those of 3-body problems (2015) (12)
Two closed geodesics on $${\mathbb {R}}P^{2n+1}$$RP2n+1 with a bumpy Finsler metric (2015) (12)
Collinear Central Configurations and Singular Surfaces in the Mass Space (2004) (12)
Geometric Characterization for Variational Minimization Solutions of the 3-Body Problem with Fixed Energy (2000) (12)
Resonance identities and stability of symmetric closed characteristics on symmetric compact star-shaped hypersurfaces (2014) (12)
Resonance identity for symmetric closed characteristics on symmetric convex Hamiltonian energy hypersurfaces and its applications (2013) (12)
Index functions for symplectic paths (2002) (11)
Non-hyperbolic closed characteristics on non-degenerate star-shaped hypersurfaces in ℝ2n (2015) (11)
Normal Forms of Symplectic Matrices (2000) (10)
The existence of two non-contractible closed geodesics on every bumpy Finsler compact space form (2017) (10)
Infinitely many periodic solution orbits of autonomous Lagrangian systems on tori (2003) (10)
Equivalence of linear stabilities of elliptic triangle solutions of the planar charged and classical three-body problems (2015) (8)
The index quasi-periodicity and multiplicity of closed geodesics (2010) (8)
Non-hyperbolic Closed Characteristics on Symmetric Compact Convex Hypersurfaces in R2n (2014) (8)
wo closed geodesics on $RP^{2n+1}$ with a bumpy Finsler metric (2015) (8)
Geometric characterizations for variational minimization solutions of the 3-body problem (1999) (7)
Linear stability of some symplectic matrices (2010) (7)
Linear stability of the elliptic relative equilibrium with (1 + n)-gon central configurations in planar n-body problem (2019) (7)
Collinear central configurations in celestial mechanics (2003) (6)
Periodic Solutions for the Generalized Anisotropic Lennard-Jones Hamiltonian (2015) (6)
Closed Characteristics on Asymmetric Convex Hypersurfaces in R2n and the Corresponding Pinching Conditions (2004) (6)
Progress in variational methods (2010) (6)
Geodesics in the compactly supported Hamiltonian diffeomorphism group (1995) (5)
Semi-Global Cooperative Output Regulation Problem for Heterogeneous Swarm Systems With Input Saturation Under Switching Network (2019) (5)
Progress In Nonlinear Analysis (2000) (5)
Collection of problems proposed at International Conference on Variational Methods (2008) (5)
Closed characteristics on compact convex hypersurfaces in $\mathbf{R}^{2n}$ (2002) (4)
Concentrated steady vorticities of the Euler equation on 2-d domains and their linear stability (2018) (4)
Index iteration theories for periodic orbits: Old and new (2020) (3)
The linear stability of elliptic Euler-Moulton solutions of the n-body problem via those of 3-body problems (2015) (3)
Index Theory for Symplectic Matrix Paths with Applications (2008) (3)
On the Density of the Range for Some Superquadratic Operators. (1985) (3)
ω-Index Theory and Linear Stability of Elliptic Lagrangian Solutions of the Classical Three-Body Problem (2012) (3)
CRITERION FOR SL(2, Z)-MATRIX TO BE CONJUGATE TO ITS INVERSE (2002) (2)
Linear Stability of Elliptic Lagrangian Solutions of the Planar Three-Body Problem via Index Theory (2014) (2)
Dynamics on compact convex hypersurfaces in2n (2000) (2)
Maslov-Type Indices and Linear Stability of Elliptic Euler Solutions of the Three-Body Problem (2017) (2)
The existence of two closed characteristics on every compact star-shaped hypersurface in ℝ4 (2014) (2)
Functions on Tori with Minimal Number of Critical Points and Rotation Type Solutions of Spatially Periodic Hamiltonian Systems (2011) (2)
Symmetric Closed Characteristics on Symmetric Compact Convex Hypersurfaces in $$\mathbf{R}^8$$R8 (2014) (2)
On bifurcation of eigenvalues along convex symplectic paths (2017) (2)
Solutions of the generalized Lennard-Jones system (2018) (2)
On the density of the range for some nonlinear operators (1989) (1)
A new index theory for GL+(2)-paths with applications to asymptotically linear systems (2017) (1)
Irrationally elliptic closed characteristics on symmetric compact star-shaped hypersurfaces in R 4 (2016) (1)
Index iteration theory for symplectic paths and multiple periodic solution orbits (2006) (1)
Ju l 2 01 6 The reduction on the linear stability of elliptic Euler-Moulton solutions of the n-body problem to those of 3-body problems (2016) (1)
A new class of problems in the calculus of variations (2013) (1)
Irrationally elliptic closed characteristics on symmetric compact star-shaped hypersurfaces in $$\mathbf{R}^\mathbf{4}$$R4 (2017) (1)
Morse Indices of Closed Geodesics on Katok's 2-Spheres (2008) (1)
Symmetric Closed Characteristics on Symmetric Compact Convex Hypersurfaces in R8\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{d (2014) (0)
ANISOTROPIC GENERALIZED LENNARD – JONES HAMILTONIAN (2016) (0)
Iteration Theory for Symplectic Paths and Periodic Solution Orbits (2008) (0)
Properties of index functions (2002) (0)
Open Problem 2: Questions on the Stability Problem of Periodic Solutions in the N-Body Problem (2015) (0)
The Rabinowitz minimal periodic solution conjecture (2021) (0)
Periodic Lagrangian orbits on tori (2002) (0)
The common index jump theorem (2002) (0)
Emerging topics on differential equations and their applications : proceedings on Sino-Japan Conference of Young Mathematicians on Emerging Topics on Differential Equations and their Applications, Nankai University, China, 5-9 December 2011 (2013) (0)
Relations with other Morse indices (2002) (0)
Economic growth and sustainable development: how should we discount the future? (2012) (0)
Hamiltonian systems and canonical transformations (2002) (0)
Research on Collision Avoidance and Vehicle Stability Control of Intelligent Driving Vehicles in Harsh Environments (2022) (0)
RECENT PROGRESS ON CLOSED GEODESICS IN SOME COMPACT SIMPLY CONNECTED MANIFOLDS (2010) (0)
Geometric characterizations for variational minimizing solutions of charged 3-body problems (2016) (0)
The variational functional (2002) (0)
Closed geodesics on 2 dimensional spheres (2005) (0)
Resonance identities and stability of symmetric closed characteristics on symmetric compact star-shaped hypersurfaces (2015) (0)
Precise iteration formulae (2002) (0)
Solutions of the generalized Lennard-Jones system (2017) (0)
S ep 2 01 6 Maslov-type indices and linear stability of elliptic Eulersolutions of the three-body problem (2018) (0)
Periodic solutions of Hamiltonian systems with prescribed energy (2016) (0)
Bott-type iteration formulae (2002) (0)
The enhanced common index jump theorem for symplectic paths and non-hyperbolic closed geodesics on Finsler manifolds (2016) (0)
The Rabinowitz conjecture (2002) (0)
Se p 20 01 Closed characteristics on compact convex hypersurfaces in R 2 n (1996) (0)
RECENT PROGRESS ON CLOSED GEODESICS IN SOME COMPACT SIMPLY CONNECTED MANIFOLDS (2010) (0)
Open Problem 2: Questions on the Stability Problem of Periodic Solutions in the N-Body Problem (2015) (0)
Generalized common index jump theorem with applications to closed characteristics on star-shaped hypersurfaces and beyond (2022) (0)
Long Multiplicity and stability of closed geodesics on Finsler 2-spheres Dedicated (2006) (0)
Periodic Solutions for the Generalized Anisotropic Lennard-Jones Hamiltonian (2015) (0)
Differentiable structure of ω-subsets of symplectic groups (2001) (0)
The reduction of the linear stability of elliptic Euler–Moulton solutions of the n-body problem to those of 3-body problems (2016) (0)
Progress in variational methods : proceedings of the International Conference on Variational Methods, Tianjin, China, 18-22 May 2009 (2011) (0)
Non-hyperbolic closed characteristics on non-degenerate star-shaped hypersurfaces in ℝ2n (2016) (0)
Geometric characterizations for variational minimizing solutions of charged 3-body problems (2016) (0)
Progress in nonlinear analysis : Proceedings of the Second International Conference on Nonlinear Analysis, Tianjin, China, 14-19 June 1999 (2000) (0)
Index iteration theory for closed geodesics (2002) (0)

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