Encyclopedia of Complexity and Systems Science

Living Edition
| Editors: Robert A. Meyers

Perturbation of Systems with Nilpotent Real Part

  • Todor Gramchev
Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27737-5_395-4

Definition of the Subject

The main goal of this entry is to dwell upon the influence of the presence (explicit and/or hidden) of nontrivial real nilpotent perturbations appearing in problems in dynamical systems, partial differential equations, and mathematical physics. Under the term nilpotent perturbation, we will mean, broadly speaking, a classical linear algebra typesetting: we start with an object (vector field or map near a fixed point, first-order singular partial differential equations, system of evolution partial differential equations) whose “linear part” A is semisimple (diagonalizable) and we add a (small) nilpotent part N. The problems of interest might be summarized as follows: are the “relevant properties” (in suitable functional framework) of the initial “object” stable under the perturbation N? If instabilities occur, to classify, if possible, the novel features of the perturbed systems.

Broadly speaking, the cases when the instabilities occur are rare; they form some...


Normal Form Jordan Block Small Divisor Convergent Power Series Normal Form Theory 
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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Dipartimento di Matematica e InformaticaUniversità di CagliariCagliariItaly