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A periodic perturbation generates a complicated dynamics close to separatrices and saddle points. We construct an asymptotic solution which is close to the separatrix for the unperturbed Duffing's oscillator over a long time. This solution…

We study the oscillations and stability of self-gravitating cylindrically symmetric fluid systems and collisionless systems. This is done by studying small perturbations to the equilibrium system and finding the normal modes, using methods…

The secular evolution of disk galaxies is largely driven by resonances between the orbits of 'particles' (stars or dark matter) and the rotation of non-axisymmetric features (spiral arms or a bar). Such resonances may also explain kinematic…

Low mass, self-gravitating accretion disks admit quasi-steady,`gravito-turbulent' states in which cooling balances turbulent viscous heating. However, numerical simulations show that gravito-turbulence cannot be sustained beyond dynamical…

Mechanical vibrations are known to affect frictional sliding and the associated stick-slip patterns causing sometimes a drastic reduction of the friction force. This issue is relevant for applications in nanotribology and to understand…

We present numerical simulations of misaligned discs around a spinning black hole covering a range of parameters. Previous simulations have shown that discs that are strongly warped by a forced precession -- in this case the Lense-Thirring…

The steady states of two vibrated granular gases separated by an adiabatic piston are investigated. The system exhibits a non-equilibrium phase transition with an spontaneous symmetry breaking. Even if the gases at both sides of the piston…

Frictional granular matter is shown to be fundamentally different in its plastic responses to external strains from generic glasses and amorphous solids without friction. While regular glasses exhibit plastic instabilities due to a…

Vibrated granular matter constitutes a useful system for studying the physics of active matter. Usually, self-propulsion is induced in grains through suitable asymmetry in the particle design. In this paper, we show that a symmetrical mini…

Nonlinear dynamics of a bouncing ball moving in gravitational field and colliding with a moving limiter is considered. Displacement of the limiter is a quadratic function of time. Several dynamical modes, such as fixed points, 2 - cycles…

In this paper, we study the indirect boundary stabilization of a Bresse system with only two dissipation laws. This system, which models the dynamics of a beam, is a hyperbolic system with three wave speeds. We study the asymptotic…

A challenge in soft robotics and soft actuation is the determination of an elastic system which spontaneously recovers its trivial path during postcritical deformation after a bifurcation. The interest in this behaviour is that a…

We investigate the frictional force arising from quantum fluctuations when two dissipative metallic plates are set in a shear motion. While early studies showed that the electromagnetic fields in the quantum friction setup reach…

Observational evidence accumulated over the past decade indicates that accretion discs in X-ray binaries are viscously stable unless they accrete very close to the Eddington limit. This is at odds with the most basic standard accretion disc…

We present a perturbation theory for studying the instabilities of non-axisymmetric gaseous discs. We perturb the dynamical equations of self-gravitating fluids in the vicinity of a non-axisymmetric equilibrium, and expand the perturbed…

We show that interacting bosons on a ring which are driven periodically by a rotating potential can support discrete time crystals whose absolute stability can be proven. The absolute stability is demonstrated by an exact mapping of…

In this paper we present an influence of discontinuous coupling on the dynamics of multistable systems. Our model consists of two periodically forced oscillators that can interact via soft impacts. The controlling parameters are the…

We provide a constructive method designed in order to control the stability of a given periodic orbit of a general completely integrable system. The method consists of a specific type of perturbation, such that the resulting perturbed…

We consider the contribution to the density of vibrational states and the distribution of energy barrier heights of incipient instabilities in a glass modeled by a jammed packing of spheres. On approaching an instability, the frequency of a…

A linear stability analysis has been performed onto a self-gravitating magnetized gas disk bounded by external pressure. The resulting dispersion relation is fully explained by three kinds of instability: a Parker-type instability driven by…