Classification of dynamical systems based on a decomposition of their vector fields

Stavros Anastassiou, Spyros Pnevmatikos, Tassos Bountis

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


We present a method for the global classification of dynamical systems based on a specific decomposition of their vector fields. Every differentiable vector field on Rn can be decomposed uniquely in the sum of 2 systems: one gradient and one that leaves invariant the spheres Sn-1. We show that, under some conditions, the topological class of a vector field is determined by the topological classes of its summands. We illustrate this method by applying it to a number of vector fields, among them being some members of the so-called Lorenz family. The advantage of such a classification is that equivalent flows exhibit qualitatively the same dynamical phenomena as their parameters are varied.

Original languageEnglish
Pages (from-to)2252-2262
Number of pages11
JournalJournal of Differential Equations
Issue number7
Publication statusPublished - Oct 1 2012

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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