1 - 10 of 11 articles
We use the theory of reduction of exterior differential systems with symmetry to study the problem of using a symmetry group of a differential equation to find noninvariant solutions.
A general analysis of special classes of symmetric two-tensor on Riemannian manifolds is provided. These tensors arise in connection with special topics in differential geometry and analytical mechanics: geodesic equivalence and separation of variables. It is shown that they play an important...
Many and important integrable Hamiltonian systems are ‘superintegrable’, in the sense that there is an open subset of their 2d-dimensional phase space in which all motions are linear on tori of dimension n
We survey and discuss Poincaré–Dulac normal forms of maps near a fixed point. The presentation is accessible with no particular prerequisites. After some introductory material and general results (mostly known facts) we turn to further normalization in the simple resonance case and to formal and...
We give an elementary introduction to exterior differential systems and the Cartan–Kähler theorem. No proofs are given, but the results are illustrated by means of examples.
This paper gives a setup for normal form theory and the computation of normal forms with emphasis on the dual character of the transformation generators and the objects to be transformed into normal form. Spectral sequence techniques will be used to define unique normal forms. Theoretical...
We review the proposal of a constructive axiomatic approach to the determination of the orbit spaces of all the real compact linear groups, obtained through the computation of a metric matrix
, which is defined only in terms of the scalar products between the gradients ∂p...
Invariant manifolds like tori, spheres and cylinders play an important part in dynamical systems. In engineering, tori correspond with the important phenomenon of multi-frequency oscillations. Normal hyperbolicity guarantees the robustness of these manifolds but in many applications weaker forms...
In this paper we study rigorous spectral theory and solvability for both the direct and inverse problems of the Dirac operator associated with the nonlinear Schrödinger equation. We review known results and techniques, as well as incorporating new ones, in a comprehensive, unified framework. We...
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