相关论文: Heteroclinic orbits, mobility parameters and stabi…

We consider a $\mathbb{Z}_{2}$-equivariant 4-dimensional system of ODEs with a smooth first integral $H$ and a saddle equilibrium state $O$. We assume that there exists a transverse homoclinic orbit $\Gamma$ to $O$ that approaches $O$ along…

When a real saddle equilibrium in a three-dimensional vector field undergoes a homoclinic bifurcation, the associated two-dimensional invariant manifold of the equilibrium closes on itself in an orientable or non-orientable way. We are…

The main goal of this paper is to understand the formation of hexagonal patterns from the dynamical transition theory point of view. We consider the transitions from a steady state of an abstract nonlinear dissipative system. To shed light…

We consider an equation for a thin-film of fluid on a rotating cylinder and present several new analytical and numerical results on steady state solutions. First, we provide an elementary proof that both weak and classical steady states…

We solve the problem of topological classification for smooth structurally stable flows on closed four-dimensional manifolds, the non-wandering set of which contains exactly two saddle equilibria, and the wandering set contains isolated…

We study a Rock-Paper-Scissors model for competing populations that exhibits travelling waves in one spatial dimension and spiral waves in two spatial dimensions. A characteristic feature of the model is the presence of a robust…

The three-body problem is famously chaotic, with no closed-form analytical solutions. However, hierarchical systems of three or more bodies can be stable over indefinite timescales. A system is considered hierarchical if the bodies can be…

Many-body localized phases retain memory of their initial conditions in disordered interacting systems with unitary dynamics. The stability of the localized phase due to the breakdown of unitarity is of relevance to experiment in the…

We study the role of the unstable equilibrium points in the transfer of matter in a galaxy using the potential of a rotating triaxial system. In particular, we study the neighbourhood of these points for energy levels and for main model…

We present a method for proving the existence of symmetric periodic, heteroclinic or homoclinic orbits in dynamical systems with the reversing symmetry. As an application we show that the Planar Restricted Circular Three Body Problem…

We study the stability in finite times of the trajectories of interacting particles. Our aim is to show that in average and uniformly in the number of particles, two trajectories whose initial positions in phase space are close, remain…

In this work we consider a two-dimensional piecewise smooth system, defined in two domains separated by the switching manifold $x=0$. We assume that there exists a piecewise-defined continuous Hamiltonian that is a first integral of the…

We show that, in the pure-quartic systems, modulation instability (MI) undergoes heteroclinic-structure transitions (HSTs) at two critical frequencies of {\omega} c1 and {\omega} c2 ( {\omega} c2 > {\omega} c1 ), which indicates that there…

This article is devoted to the study of a $2$-dimensional piecewise smooth (but possibly) discontinuous dynamical system, subject to a non-autonomous perturbation; we assume that the unperturbed system admits a homoclinic trajectory…

The gravitational three-body problem is a fundamental problem in physics and has significant applications to astronomy. Three-body configurations are often considered stable as long the system is hierarchical; that is, the two orbital…

We study the steady states and the coarsening dynamics in a one dimensional driven non-conserved system modelled by the so called driven Allen-Cahn equation, which is the standard Allen-Cahn equation with an additional driving force. In…

We prove well-posedness, partial regularity, and stability of the thin-film equation $h_t + (m(h) h_{zzz})_z = 0$ with general mobility $m(h) = h^n$ and mobility exponent $n\in (1,\tfrac{3}{2})\cup (\tfrac{3}{2},3)$ in the regime of perfect…

We are interested in stable periodic orbits for spacecrafts in the gravitational field of minor celestial bodies. The stable periodic orbits around minor celestial bodies are useful not only for the mission design of the deep space…

Stemming from the Heisenberg equations of motion, we study the time-evolution stability of the order parameters for the cold atoms on optical lattices. The requirement of this stability of the order parameters endows the phase diagram with…

We describe the asymptotic states for the solutions of a nonlocal equation of evolutionary type, which have the physical meaning of the atom dislocation function in a periodic crystal. More precisely, we can describe accurately the…