A note on the divergence-free Jacobian Conjecture in R^2

We give a shorter proof to a recent result by Neuberger, in the real case. Our result is essentially an application of the global asymptotic stability Jacobian Conjecture. We also extend some of the results presented in Neuberger

The period functions' higher order derivatives

We prove a formula for the $n$-th derivative of the period function $T$ in a period annulus of a planar differential system. For $n = 1$, we obtain Freire, Gasull and Guillamon formula for the period's first derivative \cite{FGG}. We apply such a result to hamiltonian systems with separable variables and other systems. We give some sufficient conditions for the period function of conservative second order O.D.E.'s to be convex.Comment: 2 figure

Pose and Shape Reconstruction of a Noncooperative Spacecraft Using Camera and Range Measurements

Recent interest in on-orbit proximity operations has pushed towards the development of autonomous GNC strategies. In this sense, optical navigation enables a wide variety of possibilities as it can provide information not only about the kinematic state but also about the shape of the observed object. Various mission architectures have been either tested in space or studied on Earth. The present study deals with on-orbit relative pose and shape estimation with the use of a monocular camera and a distance sensor. The goal is to develop a filter which estimates an observed satellite's relative position, velocity, attitude, and angular velocity, along with its shape, with the measurements obtained by a camera and a distance sensor mounted on board a chaser which is on a relative trajectory around the target. The filter's efficiency is proved with a simulation on a virtual target object. The results of the simulation, even though relevant to a simplified scenario, show that the estimation process is successful and can be considered a promising strategy for a correct and safe docking maneuver

An extension to the planar Markus-Yamabe Jacobian conjecture

We extend the planar Markus–Yamabe Jacobian conjecture to differential systems having Jacobian matrix with eigenvalues with negative or zero real parts