8 papers
Relative Periodic Orbits in the Gutzwiller-type Anisotropic Kepler Problem and -body Problem
Xijun Hu, Yuwei Ou, Zhiwen Qiao +1
We study the relative periodic orbits in the Gutzwiller-type anisotropic Kepler problem, which is a generalized model derived from the classical Gutzwiller anisotropic Kepler probl…
Relative Periodic Orbits in the Spatial Anisotropic Kepler Problem
Xijun Hu, Yuwei Ou, Zhiwen Qiao
The spatial anisotropic Kepler problem comes from quantum mechanics, which models electron motion in semiconductors with donor impurities and depends on the anisotropic parameter $…
ECH Constraints and Twist Dynamics in the Spatial Isosceles Three-Body Problem
Xijun Hu, Lei Liu, Yuwei Ou +2
We study dynamical constraints arising from Embedded Contact Homology (ECH) in the spatial isosceles three-body problem. For energies below the critical level, the dynamics on the…
Index theory for singular Lagrangian systems and Bessel-type differential operators
Xijun Hu, Alessandro Portaluri, Li Wu
The aim of the present manuscript is to develop an index theory for singular Lagrangian systems, with a particular focus on the important class of singular operators given by Besse…
Quantitative Linear Stability Analysis of Elliptic Relative Equilibria in the Planar N-Body Problem
Xijun Hu, Yuwei Ou, Jiexin Sun
An elliptic relative equilibrium (ERE) is a special solution of the planar -body problem generated by a central configuration. Its linear stability depends on the eccentricity $…
Relative periodic solutions in spatial Kepler problem with symmetric perturbation
Xijun Hu, Zhiwen Qiao, Guowei Yu
The spatial Kepler problem with a perturbation satisfying the rotational symmetry w.r.t. the -axis and the reflection symmetry w.r.t. the -plane, can be reduced to an Ha…
Problem of eigenvalues of stochastic Hamiltonian systems with boundary conditions and Markov chain
Tian Chen, Xijun Hu, Zhen Wu
In this paper, we study the eigenvalue problem of stochastic Hamiltonian system driven by Brownian motion and Markov chain with boundary conditions and time-dependent coefficients.…
Non-minimality and instability of brake orbits for natural Lagrangians on Riemannian manifolds
Luca Asselle, Xijun Hu, Alessandro Portaluri +1
We investigate minimality and stability of periodic brake orbits in natural Lagrangian systems on smooth Riemannian manifolds. We prove that every non-constant periodic brake orbit…