Asymptotic dynamics of a difference equation with a parabolic equilibrium

The aim of this work is the study of the asymptotic dynamical behaviour, of solutions that approach parabolic fixed points in difference equations. In one dimensional difference equations, we present the asymptotic development for positive solutions tending to the fixed point. For higher dimensions, through the study of two families of difference equations in the two and three dimensional case, we take a look at the asymptotic dynamic behaviour. To show the existence of solutions we rely on the parametrization method

Limit cycles bifurcating from a perturbed quartic center

Agraïments: The first and third authors are partially supported by the grant TIN2008-04752/TI

Alien limit cycles in Liénard equations

Agraïments: The second author thanks the Universitat de les Illes Balears (UIB) for its support as invited professor during the period November to December, 2011.This paper aims at providing an example of a family of polynomial Liénard equations exhibiting an alien limit cycle. This limit cycle is perturbed from a 2-saddle cycle in the boundary of an annulus of periodic orbits given by a Hamiltonian vector field. The Hamiltonian represents a truncated pendulum of degree 4. In comparison to a former polynomial example, not only the equations are simpler but a lot of tedious calculations can be avoided, making the example also interesting with respect to simplicity in treatment

Periodic orbits for perturbed non-autonomous differential equations

AbstractWe consider non-autonomous differential equations, on the cylinder (t,r)∈S1×Rd, given by dr/dt=f(t,r,ε) and having an open continuum of periodic solutions when ε=0. From the study of the variational equations of low order we obtain successive functions such that the simple zeroes of the first one that is not identically zero control the periodic orbits that persist for the unperturbed equation. We apply these results to several families of differential equations with d=1,2,3. They include some autonomous polynomial differential equations and some Abel type non-autonomous differential equations

HYPERSPECTRAL AND MULTISPECTRAL WASSERSTEIN BARYCENTER FOR IMAGE FUSION

International audienceThe fusion of hyperspectral and multispectral images is a crucial task nowadays for it allows the extraction of relevant information from the fused image. Fusion consists of the combination of the spectral information of the hypespectral image (h) and the spatial information of the multispectral image (m). The fused image (f) has both good spatial and spectral information. In this paper we suggest a new hyperspectral and multispectral image (h-m) fusion approach based on Optimal Transport (OT) which highlights the idea of energy transfer from the starting images m and h to the resulting image f. The simulations show that the suggested method is effective and compares competitively with other state-of-the-art methods

A non-local algorithm for image denoising

We propose a new measure, the method noise, to evaluate and compare the performance of digital image denoising methods. We first compute and analyze this method noise for a wide class of denoising algorithms, namely the local smoothing filters. Second, we propose a new algorithm, the non local means (NL-means), based on a non local averaging of all pixels in the image. Finally, we present some experiments comparing the NL-means algorithm and the local smoothing filters. 1