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Lagrange's discrete model of the wave equation in dimension greater than one
Massimo Villarini
A celebrated theorem of Lagrange states that a solution of the wave equation with one-dimensional space variable is the uniform limit, as N tends to infinity, of a second order ODE…
A global isochronous center is linear
Massimo Villarini
Let be a polynomial vector field in which, after one-point compactification of the plane, has a punctured neighbourhood of the point at infinity which i…
On a rigidity property of perturbations of circle bundles on 3-manifolds
Massimo Villarini
We show that a smooth 1-parameter family of foliations by circles of a closed 3-manifold, deforming the foliation whose leaves are the fibers of a circle bundle, is trivial, i.e. a…
Smooth circle actions on with unbounded periods and non-linearizable multicentres
Massimo Villarini
We will give an example of a smooth free action of on whose orbits have unbounded lenghts (equivalently: unbounded periods). As an application of this example we c…
Normalization of Poincaré Singularities {\it via} Variation of Constants
T. Carletti, A. Margheri, M. Villarini
We present a geometric proof of the Poincaré-Dulac Normalization Theorem for analytic vector fields with singularities of Poincaré type. Our approach allows us to relate the size o…