1 - 10 of 11 articles
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 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.
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...
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...
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...
The analogy between monodromy in dynamical (Hamiltonian) systems and defect in crystal lattices is used in order to formulate some general conjectures about possible types of qualitative features of quantum systems which can be interpreted as a manifestation of classical monodromy in quantum...
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...
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...
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...
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