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math.DS2023
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…
math.DS2017★ 1 cited
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…
math.DS2004
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…