Geometrical conditions for the stability of orbits in planar systems

R. A. Garcia, A. Gasull, A. Guillamon

Research output: Contribution to journalArticleResearchpeer-review

3 Citations (Scopus)


Given a vector field X on the real plane, we study the influence of the curvature of the orbits of ẋ = X⊥(x) in the stability of those of the system ẋ = X(x). We pay special attention to the case in which this curvature is negative in the whole plane. Under this assumption, we classify the possible critical points and give a criterion for a point to be globally asymptotically stable. In the general case, we also provide expressions for the first three derivatives of the Poincaré map associated to a periodic orbit in terms of geometrical quantities.
Original languageEnglish
Pages (from-to)499-519
JournalMathematical Proceedings of the Cambridge Philosophical Society
Issue number3
Publication statusPublished - 1 Oct 1996


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