Related papers: Small-scale instabilities in dynamical systems wit…
Periodic orbits and cycles, respectively, play a significant role in discrete- and continuous-time dynamical systems (i.e. maps and flows). To succinctly describe their shifts when the system is applied perturbation, the notions of…
We consider the three dimensional gravitational Vlasov-Poisson (GVP) system in both classical and relativistic cases. The classical problem is subcritical in the natural energy space and the stability of a large class of ground states has…
Dynamics of regular clusters of many non-touching particles falling under gravity in a viscous fluid at low Reynolds number are analysed within the point-particle model. Evolution of two families of particle configurations is determined: 2…
Planar sliding of objects is modeled and analyzed. The model can be used for non-prehensile manipulation of objects lying on a surface. We study possible motions generated by frictional contacts, such as those arising between a soft finger…
We carried out a fluid dynamical simulation for a forced dripping faucet system using a new algorithm that was recently developed. The simulation shows that periodic external forcing induces transitions from chaotic to periodic motion and…
Closely-packed multi-planet systems are known to experience dynamical instability if the spacings between the planets are too small. Such instability can be tempered by the frictional forces acting on the planets from gaseous discs. A…
We consider the stability of periodic gravity free-surface water waves traveling downstream at a constant speed over a shear flow of finite depth. In case the free surface is flat, a sharp criterion of linear instability is established for…
Species diversity in ecosystems is often accompanied by the self-organisation of the population into fascinating spatio-temporal patterns. Here, we consider a two-dimensional three-species population model and study the spiralling patterns…
When an amorphous solid is deformed cyclically, it may reach a steady state in which the paths of constituent particles trace out closed loops that repeat in each driving cycle. A remarkable variant has been noticed in simulations where the…
The motion of a satellite around a planet can be studied by the Hill model, which is a modification of the restricted three body problem pertaining to motion of a satellite around a planet. Although the dynamics of the circular Hill model…
We consider the set of bimodal linear systems consisting of two linear dynamics acting on each side of a given hyperplane, assuming continuity along the separating hyperplane. Focusing on the unobservable planar ones, we obtain a simple…
We study the drift of slow variables in a slow-fast Hamiltonian system with several fast and slow degrees of freedom. For any periodic trajectory of the fast subsystem with the frozen slow variables we define an action. For a family of…
This paper concerns the small-time stabilization of some classes of mechanical systems which are not stabilizable by means of at least continuous state feedback laws. This is the case of nonholonomic mechanical systems, an example being the…
High-multiplicity Kepler systems (referred to as Kepler multis) are often tightly packed and may be on the verge of instability. Many systems of this type could have experienced past instabilities, where the compact orbits and often low…
We study the orbital architecture of multi-planet systems detected by the Kepler transit mission using N-body simulations, focusing on the orbital spacing between adjacent planets in systems showing four or more transiting planets. We find…
We study non oscillating bifurcations of non homogeneous steady states of the Vlasov equation, a situation occurring in galactic models, or for Bernstein-Greene-Kruskal modes in plasma physics. We show that resonances are strongly…
We consider the stability of periodic map with period-$2$ in linear fractional difference equations where the function is $f(x)=ax$ at even times and $f(x)=bx$ at odd times. The stability of such a map for an integer order map depends on…
We consider a system of four one-dimensional inelastic hard spheres evolving on the real line $\mathbb{R}$, and colliding according to a scattering law characterized by a fixed restitution coefficient $r$. We study the possible orders of…
We study persistence of periodic and homoclinic orbits, first integrals and commutative vector fields in dynamical systems depending on a small parameter $\varepsilon>0$ and give several necessary conditions for their persistence. Here we…
The cyclicity problem, crucial in analyzing planar vector fields, consists in estimating the number of limit cycles emanating from monodromic singularities. Traditionally, this estimation relies on Lyapunov coefficients. However, in…