Kramár, Miroslav Generic and stability properties of reciprocal and pseudogradient vector fields. (English) Zbl 1096.34032 Math. Slovaca 54, No. 4, 349-368 (2004). Motivated by a paper of O. Chua from 1992, the paper studies pseudoreciprocal vector fields. First, a Kupka-Smale-like theorem is proved. Then, stability results are derived for such second-order ODEs. Finally, a result on the nonexistence of periodic solutions is shown for pseudogradient vector fields on manifolds. Reviewer: Michal Fečkan (Bratislava) MSC: 34D30 Structural stability and analogous concepts of solutions to ordinary differential equations 37C20 Generic properties, structural stability of dynamical systems Keywords:generic properties; pseudoreciprocal vector field; stability × Cite Format Result Cite Review PDF Full Text: EuDML References: [1] ABRAHAM R.-ROBBIN R.: Transversal Mappings and Flows,/. Benjamin, New York-Amsterdam, 1967. · Zbl 0171.44404 [2] CHUA O.: The identification of generic pseudoreciprocal vector fields. IEEE Trans. Circuits Systems I Fund. Theory Appl. 39 (1992), 102-123. · Zbl 0748.94013 · doi:10.1109/81.167017 [3] GOLUBITSKY M.-GUILLEMIN V.: Stable Mapings and Their Singularities. Springer-Verlag, New York-Heidelberg-Berlin, 1973. · Zbl 0294.58004 [4] GUCKENHEIMER J.-HOLMES, CH.: Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields. Springer-Verlag, New York-Heidelberg-Berlin, 1983. · Zbl 0515.34001 [5] MEDVEĎ M.: Fundamentals of Dynamical Systems and Bifurcation Theory. Adam Hilger, Bristol, 1992. · Zbl 0777.58027 [6] PALIS J.-MELO W. D.: Generic Theory of Dynamical Systems. An Interduction. Springer-Verlag, New York-Heidelberg-Berlin, 1982. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.