15 citations · 51 across the 14 of their papers we have counts for
14 papers
Square Roots of Symplectic Matrices
Qinglong Zhou
This paper characterizes the existence of real symplectic square roots for symplectic matrices. The decomposition of Wonenburger matrices with respect to their eigenvalues permits…
The positive fundamental group of
Jian Wang, Qinglong Zhou
In this paper, we examine the homotopy classes of positive loops in . We demonstrate that two positive loops are homotopic if and only if they are homotopic through p…
Linear stability of the elliptic relative equilibria for the restricted N-body problem: two special cases
Jiashengliang Xie, Bowen Liu, Qinglong Zhou
In this paper, we consider the elliptic relative equilibria of the restricted -body problems, where the primaries form an Euler-Moulton collinear central configuration or…
Linear stability of the elliptic relative equilibria for the restricted -body problem: the Euler case
Bowen Liu, Qinglong Zhou
In this paper, we consider the elliptic relative equilibria of the restricted -body problems, where the three primaries form an Euler collinear configuration and the four bodies…
The symplectic reduction of the linearized Hamiltonian systems at elliptic relative equilibria of four-body problem
Qinglong Zhou
In this paper, we consider the elliptic relative equilibria of four-body problem. Here we prove that the corresponding linearized Hamiltonian system at such an elliptic relative eq…
Linear stability of elliptic relative equilibria of four-body problem with two infinitesimal masses
Qinglong Zhou
In this paper, we consider the elliptic relative equilibria of four-body problem with two infinitesimal masses. The most interesting case is when the two small masses tend to the s…
Trace estimation of a family of periodic Sturm-Liouville operators with application to Robe's restricted three-body problem
Qinglong Zhou
In this paper, we consider a family of Sturm-Liouville operators on the -periodic domain. The bifurcation with respect to the parameter region is studied, and the elliptic regio…
Linear Stability of Elliptic Relative Equilibria of Restricted Four-body Problem
Bowen Liu, Qinglong Zhou
In this paper, we consider the linear stability of the elliptic relative equilibria of the restricted 4-body problems where the three primaries form a Lagrangian triangle. By reduc…
Time-Inconsistent Stochastic Linear-quadratic Differential Game
Qinglong Zhou, Gaofeng Zong
We consider a general time-inconsistent stochastic linear-quadratic differential game. The time-inconsistency arises from the presence of quadratic terms of the expected state as w…
The analytical aspect to the linear stability of elliptic equilibrium points of the Robe's restricted three-body problem
Qinglong Zhou, Yongchao Zhang
We study the Robe's restricted three-body problem. Such a motion was firstly studied by A. G. Robe in \cite{Robe}, which is used to model small oscillations of the earth's inner co…
The reduction on the linear stability of elliptic Euler-Moulton solutions of the n-body problem to those of 3-body problems
Qinglong Zhou, Yiming Long
In this paper, we consider the elliptic collinear solutions of the classical -body problem, where the bodies always stay on a straight line, and each of them moves on its ow…
A New Class of Problems in the Calculus of Variations
Ivar Ekeland, Yiming Long, Qinglong Zhou
This paper investigates an infinite-horizon problems in the one-dimensional calculus of variations, arising from the Ramsey model of endogeneous economic growth. Following Chichiln…
Equivalence of linear stabilities of elliptic triangle solutions of the planar charged and classical three-body problems
Qinglong Zhou, Yiming Long
In this paper, we prove that the linearized system of elliptic triangle homographic solution of planar charged three-body problem can be transformed to that of the elliptic equilat…
Maslov-type indices and linear stability of elliptic Euler solutions of the three-body problem
Qinglong Zhou, Yiming Long
In this paper, we use the central configuration coordinate decomposition to study the linearized Hamiltonian system near the elliptic Euler solutions. Then using the Maslov-type ω-…