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In this paper we will present some results concerning long time stability in nonlinear perturbations of resonant linear PDE's with discrete spectrum. In particular we will prove that if the perturbation satisfies a suitable nondegeneracy condition then there exists a periodic like trajectory,...
We discuss the convergence problem for coordinate transformations which take a given vector field into Poincaré–Dulac normal form. We show that the presence of linear or nonlinear Lie point symmetries can guarantee convergence of these normalizing transformations in a number of scenarios. As an...
The problem of a local classification of vector fields is considered. A construction of formal and C
∞-normal forms is described.
We consider alternative descriptions for quantum equations of motion, in analogy with classical bi-Hamiltonian systems.
We give an introduction to noncommutative geometry and to some of its applications. Emphasis will be on noncommutative manifolds, notably noncommutative tori and spheres.
The characterization of systems of differential equations admitting a superposition function allowing us to write the general solution in terms of any fundamental set of particular solutions is discussed. These systems are shown to be related with equations on a Lie group and with some...
The pseudo-rigid body model is viewed within the context of continuum mechanics and elasticity theory. A Lagrangian reduction, based on variational principles, is developed for both anisotropic and isotropic pseudo-rigid bodies. For isotropic Lagrangians, the reduced equations of motion for the...
Functions which are covariant or invariant under the transformations of a reductive linear algebraic group can be advantageously expressed in terms of functions defined in the orbit space of the group, i.e. as functions of a finite set of basic invariant polynomials. This fact and the tools of...
A large number of mathematical questions are related to problems of parametric and autoparametric resonance in engineering models. The linearized problems generally produce systems of differential equations with periodic coefficients with special stability and genericity questions. We start by...
Symmetry introduces degeneracies in dynamical systems, as well as in bifurcation problems. An “obvious” idea in order to remove these degeneracies is to project the dynamics onto the quotient space obtained by identifying points in phase space which lie in the same group orbits (the so-called...
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