An algebro-geometric classification of spectral types of equilibria
Abstract
We give three algebraic equations which allow a geometric classification of all spectral types of equilibria of a given -dimensional dynamical system, and we analyse them thoroughly in dimension 3 and 4. The loci defined by these equations correspond to definite types of bifurcations. The complement of such loci give a geometric decomposition of the space of invariants in open domains in which the equilibrium has a given spectral types. The usefulness of this approach lays in the fact that, when dealing with a parameter-dependent dynamical system, the pull-back of the loci from the space of invariants to the parameter space gives the bifurcation-decomposition of parameter space for the dynamical system at hand. We also give effective methods to explicitly compute the spectral indices.
Keywords
Cite
@article{arxiv.2012.03024,
title = {An algebro-geometric classification of spectral types of equilibria},
author = {Andrea Giacobbe},
journal= {arXiv preprint arXiv:2012.03024},
year = {2020}
}
Comments
13 pages, 9 figures. We have added section 7, corrected typos in figure 4, slightly changed the title to emphasise that the algebraic component of the work is consistent, we have corrected the style of some sentences and added considerations on a further decomposition of the discriminant variety