Ideal Systems and Connecting Orbits

In this paper,we study a class of dynamical systems in R n — ideal systems and give an existence criterion of quasi-connecting orbits for such systems. Also, an existence criterion of connecting orbits for general systems is given.

THE EXISTENCE OF CONNECTING ORBITS

In this paper,using the notion of an isolating block and Conley’s attractor theory,an existence criterion of trajectories connecting a pair of invariant sets of ordinary differential equations is given.

EXISTENCE OF BOUNDED SOLUTIONS ON THE REAL LINE FOR LINARD SYSTEM

The existence of monotone and non_monotone solutions of boundary value problem on the real line for Liénard equation is studied. Applying the theory of planar dynamical systems and the comparison method of vector fields defined by Liénard system and the system given by symmetric transformation or quasi_symmetric transformation, the invariant regions of the system are constructed. The existence of connecting orbits can be proved. A lot of sufficient conditions to guarantee the existence of solutions of the boundary value problem are obtained. Especially, when the source function is bi_stable, the existence of infinitely many monotone solusion is obtained.

THE EXISTENCE OF ORBITS CONNECTING CRITICAL POINTS OF DIFFERENTIAL EQUATIONS DEPENDING ON A PARAMETER

Using the concept of an isolated invariant set, some existence criteria of orbits connecting two critical points bifurcating from a single critical point for ordinary differential equations depending on a parameter are given.

Equilibrium configurations of the tethered three-body formation system and their nonlinear dynamics

This paper considers nonlinear dynamics of teth- ered three-body formation system with their centre of mass staying on a circular orbit around the Earth, and applies the theory of space manifold dynamics to deal with the nonlinear dynamical behaviors of the equilibrium configurations of the system. Compared with the classical circular restricted three body system, sixteen equilibrium configurations are obtained globally from the geometry of pseudo-potential energy sur- face, four of which were omitted in the previous research. The periodic Lyapunov orbits and their invariant manifolds near the hyperbolic equilibria are presented, and an iteration procedure for identifying Lyapunov orbit is proposed based on the differential correction algorithm. The non-transversal intersections between invariant manifolds are addressed to generate homoclinic and heteroclinic trajectories between the Lyapunov orbits. （3,3）- and （2,1）-heteroclinic trajecto- ries from the neighborhood of one collinear equilibrium to that of another one, and （3,6）- and （2,1）-homoclinic trajecto- ries from and to the neighborhood of the same equilibrium, are obtained based on the Poincar6 mapping technique.

Kink wave determined by parabola solution of a nonlinear ordinary differential equation

By finding a parabola solution connecting two equilibrium points of a planar dynamical system, the existence of the kink wave solution for 6 classes of nonlinear wave equations is shown. Some exact explicit parametric representations of kink wave solutions are given. Explicit parameter conditions to guarantee the existence of kink wave solutions are determined.

Spin-dependent thermoelectric effect and spin battery mechanism in triple quantum dots with Rashba spin-orbital interaction

We have studied spin-dependent thermoelectric transport through parallel triple quantum dots with Rashba spinorbital interaction（RSOI） embedded in an Aharonov-Bohm interferometer connected symmetrically to leads using nonequilibrium Green＇s function method in the linear response regime.Under the appropriate configuration of magnetic flux phase and RSOI phase,the spin figure of merit can be enhanced and is even larger than the charge figure of merit.In particular,the charge and spin thermopowers as functions of both the magnetic flux phase and the RSOI phase present quadruple-peak structures in the contour graphs.For some specific configuration of the two phases,the device can provide a mechanism that converts heat into a spin voltage when the charge thermopower vanishes while the spin thermopower is not zero,which is useful in realizing the thermal spin battery and inducing a pure spin current in the device.

On c-equivalence

In this paper,we propose some c-equivalence specifically for autonomous Lagrangian systems and show how to construct connecting orbits in energy surface based on this c-equivalence.

BIFURCATION OF BOUNDED SOLUTIONS TO ORDINARY DIFFERENTIAL EQUATIONS DEPENDING ON A PARAMETER

Using the notion of an isolated invariant set and an isolating block, an existence criterion of bifurcation points of nonstationary bounded solutions to ordinary differential systems depending on a parameter is given.

SU(2) symmetry in a Hubbard model with spin-orbit coupling

We study the underlying symmetry in a spin-orbit coupled tight-binding model with Hubbard interaction.It is shown that,in the absence of the on-site interaction,the system possesses the SU(2)symmetry arising from the time reversal symmetry.The influence of the on-site interaction on the symmetry depends on the topology of the networks:The SU(2)symmetry is shown to be the spin rotation symmetry of a simply-connected lattice even in the presence of the Hubbard interaction.On the contrary,the on-site interaction breaks the SU(2)symmetry of a multi-connected lattice.This fact indicates that a discrete spin-orbit coupled system has exclusive features from its counterpart in a continuous system.The obtained rigorous result is illustrated by a simple ring system.