arXiv subjects

Anna Maria Cherubini

Publications and source records attributed to Anna Maria Cherubini.

4 recordsLinked to original sources

arXiv2024

Energy Transport in Random Perturbations of Mechanical Systems

We describe a mechanism for transport of energy in a mechanical system consisting of a pendulum and a rotator subject to a random perturbation. The perturbation that we consider is the product of a Hamiltonian vector field and a scalar, continuous, stationary Gaussian process with Hölder continuous realizations, scaled by a smallness parameter. We show that for almost every realization of the stochastic process, there is a distinguished set of times for which there exists a random normally hyperbolic invariant manifold with associated stable and unstable manifolds that intersect transversally, for all sufficiently small values of the smallness parameter. We derive the existence of orbits along which the energy changes over time by an amount proportional to the smallness parameter. This result is related to the Arnold diffusion problem for Hamiltonian systems, which we treat here in the random setting.

math.DS↗

arXiv2024

Exploration of billiards with Keplerian potential

We study a class of elliptic billiards with a Keplerian potential inside, considering two cases: a reflective one, where the particle reflects elastically on the boundary, and a refractive one, where the particle can cross the billiard's boundary entering a region with a harmonic potential. In the latter case the dynamics is therefore given by concatenations of inner and outer arcs, connected by a refraction law. In recent papers (e.g. arXiv:2105.02108, arXiv:2108.11159, arXiv:2212.01150, arXiv:2110.03376) these billiards have been extensively studied in order to identify which conditions give rise to either regular or chaotic dynamics. In this paper we complete the study by analysing the non focused reflective case, thus complementing the results obtained in arXiv:2110.03376 in the focused one. We then analyse the focused and non focused refractive case, where no results on integrability are known except for the centred circular case, by providing an extensive numerical analysis. We present also a theoretical result regarding the linear stability of homothetic equilibrium orbits in the reflective case for general ellipses, highlighting the possible presence of bifurcations even in the integrable framework.

math.DS↗

arXiv2015

A random dynamical systems perspective on stochastic resonance

We study stochastic resonance in an over-damped approximation of the stochastic Duffing oscillator from a random dynamical systems point of view. We analyse this problem in the general framework of random dynamical systems with a nonautonomous forcing. We prove the existence of a unique global attracting random periodic orbit and a stationary periodic measure. We use the stationary periodic measure to define an indicator for the stochastic resonance.

math.DS↗

arXiv2007

On the Stopping Time of a Bouncing Ball

We study a simple model of a bouncing ball that takes explicitely into account the elastic deformability of the body and the energy dissipation due to internal friction. We show that this model is not subject to the problem of inelastic collapse, that is, it does not allow an infinite number of impacts in a finite time. We compute asymptotic expressions for the time of flight and for the impact velocity. We also prove that contacts with zero velocity of the lower end of the ball are possible, but non-generic. Finally, we compare our findings with other models and laboratory experiments.

math-ph↗